author  berghofe 
Fri, 18 Aug 2006 17:03:23 +0200  
changeset 20397  243293620225 
parent 20376  53b31f7c1d87 
child 20411  dd8a1cda2eaf 
permissions  rwrr 
19494  1 
(* Title: HOL/Nominal/nominal_package.ML 
2 
ID: $Id$ 

3 
Author: Stefan Berghofer and Christian Urban, TU Muenchen 

4 

5 
Nominal datatype package for Isabelle/HOL. 

6 
*) 

17870  7 

8 
signature NOMINAL_PACKAGE = 

9 
sig 

10 
val add_nominal_datatype : bool > string list > (string list * bstring * mixfix * 

18068  11 
(bstring * string list * mixfix) list) list > theory > theory 
17870  12 
end 
13 

18068  14 
structure NominalPackage : NOMINAL_PACKAGE = 
17870  15 
struct 
16 

17 
open DatatypeAux; 

18068  18 
open NominalAtoms; 
17870  19 

18016  20 
(** FIXME: DatatypePackage should export this function **) 
21 

22 
local 

23 

24 
fun dt_recs (DtTFree _) = [] 

25 
 dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts) 

26 
 dt_recs (DtRec i) = [i]; 

27 

28 
fun dt_cases (descr: descr) (_, args, constrs) = 

29 
let 

30 
fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i))); 

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val bnames = map the_bname (distinct op = (List.concat (map dt_recs args))); 
18016  32 
in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end; 
33 

34 

35 
fun induct_cases descr = 

36 
DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr))); 

37 

38 
fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i)); 

39 

40 
in 

41 

42 
fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); 

43 

44 
fun mk_case_names_exhausts descr new = 

45 
map (RuleCases.case_names o exhaust_cases descr o #1) 

46 
(List.filter (fn ((_, (name, _, _))) => name mem_string new) descr); 

47 

48 
end; 

49 

50 
(*******************************) 

51 

17870  52 
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); 
53 

54 
fun read_typ sign ((Ts, sorts), str) = 

55 
let 

56 
val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =) 

57 
(map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg 

58 
in (Ts @ [T], add_typ_tfrees (T, sorts)) end; 

59 

60 
(** taken from HOL/Tools/datatype_aux.ML **) 

61 

62 
fun indtac indrule indnames i st = 

63 
let 

64 
val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); 

65 
val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop 

66 
(Logic.strip_imp_concl (List.nth (prems_of st, i  1)))); 

67 
val getP = if can HOLogic.dest_imp (hd ts) then 

68 
(apfst SOME) o HOLogic.dest_imp else pair NONE; 

69 
fun abstr (t1, t2) = (case t1 of 

70 
NONE => (case filter (fn Free (s, _) => s mem indnames  _ => false) 

71 
(term_frees t2) of 

72 
[Free (s, T)] => absfree (s, T, t2) 

73 
 _ => sys_error "indtac") 

74 
 SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2))) 

75 
val cert = cterm_of (Thm.sign_of_thm st); 

76 
val Ps = map (cert o head_of o snd o getP) ts; 

77 
val indrule' = cterm_instantiate (Ps ~~ 

78 
(map (cert o abstr o getP) ts')) indrule 

79 
in 

80 
rtac indrule' i st 

81 
end; 

82 

18658  83 
fun mk_subgoal i f st = 
84 
let 

85 
val cg = List.nth (cprems_of st, i  1); 

86 
val g = term_of cg; 

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val revcut_rl' = Thm.lift_rule cg revcut_rl; 

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val v = head_of (Logic.strip_assums_concl (hd (prems_of revcut_rl'))); 

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val ps = Logic.strip_params g; 

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val cert = cterm_of (sign_of_thm st); 

91 
in 

92 
compose_tac (false, 

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Thm.instantiate ([], [(cert v, cert (list_abs (ps, 

94 
f (rev ps) (Logic.strip_assums_hyp g) (Logic.strip_assums_concl g))))]) 

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revcut_rl', 2) i st 

96 
end; 

97 

98 
(** simplification procedure for sorting permutations **) 

99 

100 
val dj_cp = thm "dj_cp"; 

101 

102 
fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]), 

103 
Type ("fun", [_, U])])) = (T, U); 

104 

19494  105 
fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u 
18658  106 
 permTs_of _ = []; 
107 

19494  108 
fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) = 
18658  109 
let 
110 
val (aT as Type (a, []), S) = dest_permT T; 

111 
val (bT as Type (b, []), _) = dest_permT U 

112 
in if aT mem permTs_of u andalso aT <> bT then 

113 
let 

114 
val a' = Sign.base_name a; 

115 
val b' = Sign.base_name b; 

116 
val cp = PureThy.get_thm thy (Name ("cp_" ^ a' ^ "_" ^ b' ^ "_inst")); 

117 
val dj = PureThy.get_thm thy (Name ("dj_" ^ b' ^ "_" ^ a')); 

118 
val dj_cp' = [cp, dj] MRS dj_cp; 

119 
val cert = SOME o cterm_of thy 

120 
in 

121 
SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)] 

122 
[cert t, cert r, cert s] dj_cp')) 

123 
end 

124 
else NONE 

125 
end 

126 
 perm_simproc' thy ss _ = NONE; 

127 

128 
val perm_simproc = 

129 
Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \\<bullet> (pi2 \\<bullet> x)"] perm_simproc'; 

130 

131 
val allE_Nil = read_instantiate_sg (the_context()) [("x", "[]")] allE; 

132 

133 
val meta_spec = thm "meta_spec"; 

134 

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fun projections rule = 
19874  136 
ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule 
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> map (standard #> RuleCases.save rule); 
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provide projections of induct_weak, induct_unsafe;
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20267  139 
val supp_prod = thm "supp_prod"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val fresh_prod = thm "fresh_prod"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val supports_fresh = thm "supports_fresh"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val supports_def = thm "Nominal.op supports_def"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val fresh_def = thm "fresh_def"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val supp_def = thm "supp_def"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val rev_simps = thms "rev.simps"; 
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Finished implementation of uniqueness proof for recursion combinator.
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val app_simps = thms "op @.simps"; 
20267  147 

17870  148 
fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy = 
149 
let 

150 
(* this theory is used just for parsing *) 

151 

152 
val tmp_thy = thy > 

153 
Theory.copy > 

154 
Theory.add_types (map (fn (tvs, tname, mx, _) => 

155 
(tname, length tvs, mx)) dts); 

156 

157 
val sign = Theory.sign_of tmp_thy; 

158 

159 
val atoms = atoms_of thy; 

160 
val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms; 

161 
val cp_classes = List.concat (map (fn atom1 => map (fn atom2 => 

162 
Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^ 

163 
Sign.base_name atom2)) atoms) atoms); 

164 
fun augment_sort S = S union classes; 

165 
val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S)); 

166 

167 
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) = 

168 
let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs) 

169 
in (constrs @ [(cname, cargs', mx)], sorts') end 

170 

171 
fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) = 

172 
let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs) 

173 
in (dts @ [(tvs, tname, mx, constrs')], sorts') end 

174 

175 
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts); 

176 
val sorts' = map (apsnd augment_sort) sorts; 

177 
val tyvars = map #1 dts'; 

178 

179 
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts'; 

180 
val constr_syntax = map (fn (tvs, tname, mx, constrs) => 

181 
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; 

182 

183 
val ps = map (fn (_, n, _, _) => 

184 
(Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts; 

185 
val rps = map Library.swap ps; 

186 

19494  187 
fun replace_types (Type ("Nominal.ABS", [T, U])) = 
188 
Type ("fun", [T, Type ("Nominal.noption", [replace_types U])]) 

17870  189 
 replace_types (Type (s, Ts)) = 
190 
Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts) 

191 
 replace_types T = T; 

192 

193 
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn, 

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 Changed naming scheme: names of "internal" constructors now have
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194 
map (fn (cname, cargs, mx) => (cname ^ "_Rep", 
17870  195 
map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts'; 
196 

197 
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; 

198 
val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names'; 

199 

18045  200 
val ({induction, ...},thy1) = 
17870  201 
DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy; 
202 

203 
val SOME {descr, ...} = Symtab.lookup 

204 
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names'); 

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Added strong induction theorem (currently only axiomatized!).
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205 
fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i); 
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Added strong induction theorem (currently only axiomatized!).
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206 

17870  207 
(**** define permutation functions ****) 
208 

209 
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); 

210 
val pi = Free ("pi", permT); 

211 
val perm_types = map (fn (i, _) => 

212 
let val T = nth_dtyp i 

213 
in permT > T > T end) descr; 

19494  214 
val perm_names = replicate (length new_type_names) "Nominal.perm" @ 
17870  215 
DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1) 
216 
("perm_" ^ name_of_typ (nth_dtyp i))) 

217 
(length new_type_names upto length descr  1)); 

218 
val perm_names_types = perm_names ~~ perm_types; 

219 

220 
val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) => 

221 
let val T = nth_dtyp i 

222 
in map (fn (cname, dts) => 

223 
let 

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224 
val Ts = map (typ_of_dtyp descr sorts') dts; 
17870  225 
val names = DatatypeProp.make_tnames Ts; 
226 
val args = map Free (names ~~ Ts); 

227 
val c = Const (cname, Ts > T); 

228 
fun perm_arg (dt, x) = 

229 
let val T = type_of x 

230 
in if is_rec_type dt then 

231 
let val (Us, _) = strip_type T 

232 
in list_abs (map (pair "x") Us, 

233 
Const (List.nth (perm_names_types, body_index dt)) $ pi $ 

234 
list_comb (x, map (fn (i, U) => 

19494  235 
Const ("Nominal.perm", permT > U > U) $ 
17870  236 
(Const ("List.rev", permT > permT) $ pi) $ 
237 
Bound i) ((length Us  1 downto 0) ~~ Us))) 

238 
end 

19494  239 
else Const ("Nominal.perm", permT > T > T) $ pi $ x 
17870  240 
end; 
241 
in 

242 
(("", HOLogic.mk_Trueprop (HOLogic.mk_eq 

243 
(Const (List.nth (perm_names_types, i)) $ 

244 
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ 

245 
list_comb (c, args), 

246 
list_comb (c, map perm_arg (dts ~~ args))))), []) 

247 
end) constrs 

248 
end) descr); 

249 

20179  250 
val (perm_simps, thy2) = thy1 > 
17870  251 
Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn)) 
252 
(List.drop (perm_names_types, length new_type_names))) > 

19635  253 
PrimrecPackage.add_primrec_unchecked_i "" perm_eqs; 
17870  254 

255 
(**** prove that permutation functions introduced by unfolding are ****) 

256 
(**** equivalent to already existing permutation functions ****) 

257 

258 
val _ = warning ("length descr: " ^ string_of_int (length descr)); 

259 
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); 

260 

261 
val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types); 

262 
val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def"); 

263 

264 
val unfolded_perm_eq_thms = 

265 
if length descr = length new_type_names then [] 

266 
else map standard (List.drop (split_conj_thm 

20046  267 
(Goal.prove_global thy2 [] [] 
17870  268 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
269 
(map (fn (c as (s, T), x) => 

270 
let val [T1, T2] = binder_types T 

271 
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), 

19494  272 
Const ("Nominal.perm", T) $ pi $ Free (x, T2)) 
17870  273 
end) 
18010  274 
(perm_names_types ~~ perm_indnames)))) 
275 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  276 
ALLGOALS (asm_full_simp_tac 
277 
(simpset_of thy2 addsimps [perm_fun_def]))])), 

278 
length new_type_names)); 

279 

280 
(**** prove [] \<bullet> t = t ****) 

281 

282 
val _ = warning "perm_empty_thms"; 

283 

284 
val perm_empty_thms = List.concat (map (fn a => 

285 
let val permT = mk_permT (Type (a, [])) 

286 
in map standard (List.take (split_conj_thm 

20046  287 
(Goal.prove_global thy2 [] [] 
17870  288 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
289 
(map (fn ((s, T), x) => HOLogic.mk_eq 

290 
(Const (s, permT > T > T) $ 

291 
Const ("List.list.Nil", permT) $ Free (x, T), 

292 
Free (x, T))) 

293 
(perm_names ~~ 

18010  294 
map body_type perm_types ~~ perm_indnames)))) 
295 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  296 
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])), 
297 
length new_type_names)) 

298 
end) 

299 
atoms); 

300 

301 
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****) 

302 

303 
val _ = warning "perm_append_thms"; 

304 

305 
(*FIXME: these should be looked up statically*) 

306 
val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst"); 

307 
val pt2 = PureThy.get_thm thy2 (Name "pt2"); 

308 

309 
val perm_append_thms = List.concat (map (fn a => 

310 
let 

311 
val permT = mk_permT (Type (a, [])); 

312 
val pi1 = Free ("pi1", permT); 

313 
val pi2 = Free ("pi2", permT); 

314 
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); 

315 
val pt2' = pt_inst RS pt2; 

316 
val pt2_ax = PureThy.get_thm thy2 

317 
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a)); 

318 
in List.take (map standard (split_conj_thm 

20046  319 
(Goal.prove_global thy2 [] [] 
17870  320 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
321 
(map (fn ((s, T), x) => 

322 
let val perm = Const (s, permT > T > T) 

323 
in HOLogic.mk_eq 

324 
(perm $ (Const ("List.op @", permT > permT > permT) $ 

325 
pi1 $ pi2) $ Free (x, T), 

326 
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) 

327 
end) 

328 
(perm_names ~~ 

18010  329 
map body_type perm_types ~~ perm_indnames)))) 
330 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  331 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))), 
332 
length new_type_names) 

333 
end) atoms); 

334 

335 
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) 

336 

337 
val _ = warning "perm_eq_thms"; 

338 

339 
val pt3 = PureThy.get_thm thy2 (Name "pt3"); 

340 
val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev"); 

341 

342 
val perm_eq_thms = List.concat (map (fn a => 

343 
let 

344 
val permT = mk_permT (Type (a, [])); 

345 
val pi1 = Free ("pi1", permT); 

346 
val pi2 = Free ("pi2", permT); 

347 
(*FIXME: not robust  better access these theorems using NominalData?*) 

348 
val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst")); 

349 
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); 

350 
val pt3' = pt_inst RS pt3; 

351 
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); 

352 
val pt3_ax = PureThy.get_thm thy2 

353 
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a)); 

354 
in List.take (map standard (split_conj_thm 

20046  355 
(Goal.prove_global thy2 [] [] (Logic.mk_implies 
19494  356 
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq", 
17870  357 
permT > permT > HOLogic.boolT) $ pi1 $ pi2), 
358 
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

359 
(map (fn ((s, T), x) => 

360 
let val perm = Const (s, permT > T > T) 

361 
in HOLogic.mk_eq 

362 
(perm $ pi1 $ Free (x, T), 

363 
perm $ pi2 $ Free (x, T)) 

364 
end) 

365 
(perm_names ~~ 

18010  366 
map body_type perm_types ~~ perm_indnames))))) 
367 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  368 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), 
369 
length new_type_names) 

370 
end) atoms); 

371 

372 
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) 

373 

374 
val cp1 = PureThy.get_thm thy2 (Name "cp1"); 

375 
val dj_cp = PureThy.get_thm thy2 (Name "dj_cp"); 

376 
val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose"); 

377 
val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev"); 

378 
val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget"); 

379 

380 
fun composition_instance name1 name2 thy = 

381 
let 

382 
val name1' = Sign.base_name name1; 

383 
val name2' = Sign.base_name name2; 

384 
val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2'); 

385 
val permT1 = mk_permT (Type (name1, [])); 

386 
val permT2 = mk_permT (Type (name2, [])); 

387 
val augment = map_type_tfree 

388 
(fn (x, S) => TFree (x, cp_class :: S)); 

389 
val Ts = map (augment o body_type) perm_types; 

390 
val cp_inst = PureThy.get_thm thy 

391 
(Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst")); 

392 
val simps = simpset_of thy addsimps (perm_fun_def :: 

393 
(if name1 <> name2 then 

394 
let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1')) 

395 
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end 

396 
else 

397 
let 

398 
val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst")); 

399 
val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst")) 

400 
in 

401 
[cp_inst RS cp1 RS sym, 

402 
at_inst RS (pt_inst RS pt_perm_compose) RS sym, 

403 
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] 

404 
end)) 

20046  405 
val thms = split_conj_thm (Goal.prove_global thy [] [] 
17870  406 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
407 
(map (fn ((s, T), x) => 

408 
let 

409 
val pi1 = Free ("pi1", permT1); 

410 
val pi2 = Free ("pi2", permT2); 

411 
val perm1 = Const (s, permT1 > T > T); 

412 
val perm2 = Const (s, permT2 > T > T); 

19494  413 
val perm3 = Const ("Nominal.perm", permT1 > permT2 > permT2) 
17870  414 
in HOLogic.mk_eq 
415 
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), 

416 
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) 

417 
end) 

18010  418 
(perm_names ~~ Ts ~~ perm_indnames)))) 
419 
(fn _ => EVERY [indtac induction perm_indnames 1, 

20046  420 
ALLGOALS (asm_full_simp_tac simps)])) 
17870  421 
in 
19275  422 
foldl (fn ((s, tvs), thy) => AxClass.prove_arity 
17870  423 
(s, replicate (length tvs) (cp_class :: classes), [cp_class]) 
19133
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Adapted to Florian's recent changes to the AxClass package.
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diff
changeset

424 
(ClassPackage.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy) 
17870  425 
thy (full_new_type_names' ~~ tyvars) 
426 
end; 

427 

18381
246807ef6dfb
changed the types in accordance with Florian's changes
urbanc
parents:
18366
diff
changeset

428 
val (perm_thmss,thy3) = thy2 > 
17870  429 
fold (fn name1 => fold (composition_instance name1) atoms) atoms > 
430 
curry (Library.foldr (fn ((i, (tyname, args, _)), thy) => 

19275  431 
AxClass.prove_arity (tyname, replicate (length args) classes, classes) 
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

432 
(ClassPackage.intro_classes_tac [] THEN REPEAT (EVERY 
17870  433 
[resolve_tac perm_empty_thms 1, 
434 
resolve_tac perm_append_thms 1, 

435 
resolve_tac perm_eq_thms 1, assume_tac 1])) thy)) 

436 
(List.take (descr, length new_type_names)) > 

437 
PureThy.add_thmss 

438 
[((space_implode "_" new_type_names ^ "_unfolded_perm_eq", 

18759  439 
unfolded_perm_eq_thms), [Simplifier.simp_add]), 
17870  440 
((space_implode "_" new_type_names ^ "_perm_empty", 
18759  441 
perm_empty_thms), [Simplifier.simp_add]), 
17870  442 
((space_implode "_" new_type_names ^ "_perm_append", 
18759  443 
perm_append_thms), [Simplifier.simp_add]), 
17870  444 
((space_implode "_" new_type_names ^ "_perm_eq", 
18759  445 
perm_eq_thms), [Simplifier.simp_add])]; 
17870  446 

447 
(**** Define representing sets ****) 

448 

449 
val _ = warning "representing sets"; 

450 

451 
val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names 

452 
(map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr)); 

453 
val big_rep_name = 

454 
space_implode "_" (DatatypeProp.indexify_names (List.mapPartial 

19494  455 
(fn (i, ("Nominal.noption", _, _)) => NONE 
17870  456 
 (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set"; 
457 
val _ = warning ("big_rep_name: " ^ big_rep_name); 

458 

459 
fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) = 

460 
(case AList.lookup op = descr i of 

19494  461 
SOME ("Nominal.noption", _, [(_, [dt']), _]) => 
17870  462 
apfst (cons dt) (strip_option dt') 
463 
 _ => ([], dtf)) 

19494  464 
 strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) = 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

465 
apfst (cons dt) (strip_option dt') 
17870  466 
 strip_option dt = ([], dt); 
467 

19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

468 
val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts') 
18280
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

469 
(List.concat (map (fn (_, (_, _, cs)) => List.concat 
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

470 
(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

471 

17870  472 
fun make_intr s T (cname, cargs) = 
473 
let 

474 
fun mk_prem (dt, (j, j', prems, ts)) = 

475 
let 

476 
val (dts, dt') = strip_option dt; 

477 
val (dts', dt'') = strip_dtyp dt'; 

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

478 
val Ts = map (typ_of_dtyp descr sorts') dts; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

479 
val Us = map (typ_of_dtyp descr sorts') dts'; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

480 
val T = typ_of_dtyp descr sorts' dt''; 
17870  481 
val free = mk_Free "x" (Us > T) j; 
482 
val free' = app_bnds free (length Us); 

483 
fun mk_abs_fun (T, (i, t)) = 

484 
let val U = fastype_of t 

19494  485 
in (i + 1, Const ("Nominal.abs_fun", [T, U, T] > 
486 
Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t) 

17870  487 
end 
488 
in (j + 1, j' + length Ts, 

489 
case dt'' of 

490 
DtRec k => list_all (map (pair "x") Us, 

491 
HOLogic.mk_Trueprop (HOLogic.mk_mem (free', 

492 
Const (List.nth (rep_set_names, k), 

493 
HOLogic.mk_setT T)))) :: prems 

494 
 _ => prems, 

495 
snd (foldr mk_abs_fun (j', free) Ts) :: ts) 

496 
end; 

497 

498 
val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs; 

499 
val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem 

500 
(list_comb (Const (cname, map fastype_of ts > T), ts), 

501 
Const (s, HOLogic.mk_setT T))) 

502 
in Logic.list_implies (prems, concl) 

503 
end; 

504 

505 
val (intr_ts, ind_consts) = 

506 
apfst List.concat (ListPair.unzip (List.mapPartial 

19494  507 
(fn ((_, ("Nominal.noption", _, _)), _) => NONE 
17870  508 
 ((i, (_, _, constrs)), rep_set_name) => 
509 
let val T = nth_dtyp i 

510 
in SOME (map (make_intr rep_set_name T) constrs, 

511 
Const (rep_set_name, HOLogic.mk_setT T)) 

512 
end) 

513 
(descr ~~ rep_set_names))); 

514 

515 
val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) = 

516 
setmp InductivePackage.quiet_mode false 

517 
(InductivePackage.add_inductive_i false true big_rep_name false true false 

518 
ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3; 

519 

520 
(**** Prove that representing set is closed under permutation ****) 

521 

522 
val _ = warning "proving closure under permutation..."; 

523 

524 
val perm_indnames' = List.mapPartial 

19494  525 
(fn (x, (_, ("Nominal.noption", _, _))) => NONE  (x, _) => SOME x) 
17870  526 
(perm_indnames ~~ descr); 
527 

528 
fun mk_perm_closed name = map (fn th => standard (th RS mp)) 

20046  529 
(List.take (split_conj_thm (Goal.prove_global thy4 [] [] 
17870  530 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map 
531 
(fn (S, x) => 

532 
let 

533 
val S = map_term_types (map_type_tfree 

534 
(fn (s, cs) => TFree (s, cs union cp_classes))) S; 

535 
val T = HOLogic.dest_setT (fastype_of S); 

536 
val permT = mk_permT (Type (name, [])) 

537 
in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S), 

19494  538 
HOLogic.mk_mem (Const ("Nominal.perm", permT > T > T) $ 
17870  539 
Free ("pi", permT) $ Free (x, T), S)) 
18010  540 
end) (ind_consts ~~ perm_indnames')))) 
541 
(fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *) 

17870  542 
[indtac rep_induct [] 1, 
543 
ALLGOALS (simp_tac (simpset_of thy4 addsimps 

544 
(symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))), 

545 
ALLGOALS (resolve_tac rep_intrs 

546 
THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])), 

547 
length new_type_names)); 

548 

549 
(* FIXME: theorems are stored in database for testing only *) 

550 
val perm_closed_thmss = map mk_perm_closed atoms; 

18381
246807ef6dfb
changed the types in accordance with Florian's changes
urbanc
parents:
18366
diff
changeset

551 
val (_,thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4; 
17870  552 

553 
(**** typedef ****) 

554 

555 
val _ = warning "defining type..."; 

556 

18366  557 
val (typedefs, thy6) = 
558 
fold_map (fn ((((name, mx), tvs), c), name') => fn thy => 

17870  559 
setmp TypedefPackage.quiet_mode true 
560 
(TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE 

561 
(rtac exI 1 THEN 

562 
QUIET_BREADTH_FIRST (has_fewer_prems 1) 

19403  563 
(resolve_tac rep_intrs 1))) thy > (fn (r, thy) => 
17870  564 
let 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

565 
val permT = mk_permT (TFree (Name.variant tvs "'a", HOLogic.typeS)); 
17870  566 
val pi = Free ("pi", permT); 
567 
val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs; 

568 
val T = Type (Sign.intern_type thy name, tvs'); 

569 
val Const (_, Type (_, [U])) = c 

18366  570 
in apfst (pair r o hd) 
19635  571 
(PureThy.add_defs_unchecked_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals 
19494  572 
(Const ("Nominal.perm", permT > T > T) $ pi $ Free ("x", T), 
17870  573 
Const (Sign.intern_const thy ("Abs_" ^ name), U > T) $ 
19494  574 
(Const ("Nominal.perm", permT > U > U) $ pi $ 
17870  575 
(Const (Sign.intern_const thy ("Rep_" ^ name), T > U) $ 
576 
Free ("x", T))))), [])] thy) 

577 
end)) 

18366  578 
(types_syntax ~~ tyvars ~~ 
579 
(List.take (ind_consts, length new_type_names)) ~~ new_type_names) thy5; 

17870  580 

581 
val perm_defs = map snd typedefs; 

582 
val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs; 

18016  583 
val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs; 
17870  584 
val Rep_thms = map (#Rep o fst) typedefs; 
585 

18016  586 
val big_name = space_implode "_" new_type_names; 
587 

588 

17870  589 
(** prove that new types are in class pt_<name> **) 
590 

591 
val _ = warning "prove that new types are in class pt_<name> ..."; 

592 

593 
fun pt_instance ((class, atom), perm_closed_thms) = 

594 
fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...}, 

595 
perm_def), name), tvs), perm_closed) => fn thy => 

19275  596 
AxClass.prove_arity 
17870  597 
(Sign.intern_type thy name, 
598 
replicate (length tvs) (classes @ cp_classes), [class]) 

19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

599 
(EVERY [ClassPackage.intro_classes_tac [], 
17870  600 
rewrite_goals_tac [perm_def], 
601 
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1, 

602 
asm_full_simp_tac (simpset_of thy addsimps 

603 
[Rep RS perm_closed RS Abs_inverse]) 1, 

604 
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy 

605 
(Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy) 

606 
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms); 

607 

608 

609 
(** prove that new types are in class cp_<name1>_<name2> **) 

610 

611 
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; 

612 

613 
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = 

614 
let 

615 
val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2; 

616 
val class = Sign.intern_class thy name; 

617 
val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1 

618 
in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...}, 

619 
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => 

19275  620 
AxClass.prove_arity 
17870  621 
(Sign.intern_type thy name, 
622 
replicate (length tvs) (classes @ cp_classes), [class]) 

19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

623 
(EVERY [ClassPackage.intro_classes_tac [], 
17870  624 
rewrite_goals_tac [perm_def], 
625 
asm_full_simp_tac (simpset_of thy addsimps 

626 
((Rep RS perm_closed1 RS Abs_inverse) :: 

627 
(if atom1 = atom2 then [] 

628 
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, 

18016  629 
cong_tac 1, 
17870  630 
rtac refl 1, 
631 
rtac cp1' 1]) thy) 

632 
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~ 

633 
perm_closed_thms2) thy 

634 
end; 

635 

636 
val thy7 = fold (fn x => fn thy => thy > 

637 
pt_instance x > 

638 
fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss)) 

639 
(classes ~~ atoms ~~ perm_closed_thmss) thy6; 

640 

641 
(**** constructors ****) 

642 

643 
fun mk_abs_fun (x, t) = 

644 
let 

645 
val T = fastype_of x; 

646 
val U = fastype_of t 

647 
in 

19494  648 
Const ("Nominal.abs_fun", T > U > T > 
649 
Type ("Nominal.noption", [U])) $ x $ t 

17870  650 
end; 
651 

18016  652 
val (ty_idxs, _) = foldl 
19494  653 
(fn ((i, ("Nominal.noption", _, _)), p) => p 
18016  654 
 ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; 
655 

656 
fun reindex (DtType (s, dts)) = DtType (s, map reindex dts) 

657 
 reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i)) 

658 
 reindex dt = dt; 

659 

660 
fun strip_suffix i s = implode (List.take (explode s, size s  i)); 

661 

662 
(** strips the "_Rep" in type names *) 

18045  663 
fun strip_nth_name i s = 
664 
let val xs = NameSpace.unpack s; 

665 
in NameSpace.pack (Library.nth_map (length xs  i) (strip_suffix 4) xs) end; 

18016  666 

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

667 
val (descr'', ndescr) = ListPair.unzip (List.mapPartial 
19494  668 
(fn (i, ("Nominal.noption", _, _)) => NONE 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

669 
 (i, (s, dts, constrs)) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

670 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

671 
val SOME index = AList.lookup op = ty_idxs i; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

672 
val (constrs1, constrs2) = ListPair.unzip 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

673 
(map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname))) 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

674 
(foldl_map (fn (dts, dt) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

675 
let val (dts', dt') = strip_option dt 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

676 
in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

677 
([], cargs))) constrs) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

678 
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

679 
(index, constrs2)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

680 
end) descr); 
18045  681 

19489  682 
val (descr1, descr2) = chop (length new_type_names) descr''; 
18016  683 
val descr' = [descr1, descr2]; 
684 

19710  685 
fun partition_cargs idxs xs = map (fn (i, j) => 
686 
(List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs; 

687 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

688 
val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts, 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

689 
map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs)) 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

690 
(constrs ~~ idxss)))) (descr'' ~~ ndescr); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

691 

3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

692 
fun nth_dtyp' i = typ_of_dtyp descr'' sorts' (DtRec i); 
17870  693 

694 
val rep_names = map (fn s => 

695 
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; 

696 
val abs_names = map (fn s => 

697 
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; 

698 

18016  699 
val recTs' = List.mapPartial 
19494  700 
(fn ((_, ("Nominal.noption", _, _)), T) => NONE 
18016  701 
 (_, T) => SOME T) (descr ~~ get_rec_types descr sorts'); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

702 
val recTs = get_rec_types descr'' sorts'; 
18016  703 
val newTs' = Library.take (length new_type_names, recTs'); 
704 
val newTs = Library.take (length new_type_names, recTs); 

17870  705 

706 
val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names; 

707 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

708 
fun make_constr_def tname T T' ((thy, defs, eqns), 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

709 
(((cname_rep, _), (cname, cargs)), (cname', mx))) = 
17870  710 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

711 
fun constr_arg ((dts, dt), (j, l_args, r_args)) = 
17870  712 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

713 
val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts' dt) i) 
17870  714 
(dts ~~ (j upto j + length dts  1)) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

715 
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

716 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

717 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

718 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

719 
foldr mk_abs_fun 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

720 
(case dt of 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

721 
DtRec k => if k < length new_type_names then 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

722 
Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts' dt > 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

723 
typ_of_dtyp descr sorts' dt) $ x 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

724 
else error "nested recursion not (yet) supported" 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

725 
 _ => x) xs :: r_args) 
17870  726 
end 
727 

728 
val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs; 

729 
val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname); 

730 
val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname); 

731 
val constrT = map fastype_of l_args > T; 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

732 
val lhs = list_comb (Const (cname, constrT), l_args); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

733 
val rhs = list_comb (Const (cname_rep, map fastype_of r_args > T'), r_args); 
17870  734 
val def = Logic.mk_equals (lhs, Const (abs_name, T' > T) $ rhs); 
735 
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq 

736 
(Const (rep_name, T > T') $ lhs, rhs)); 

737 
val def_name = (Sign.base_name cname) ^ "_def"; 

18366  738 
val ([def_thm], thy') = thy > 
17870  739 
Theory.add_consts_i [(cname', constrT, mx)] > 
740 
(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)] 

741 
in (thy', defs @ [def_thm], eqns @ [eqn]) end; 

742 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

743 
fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), ((((((_, (_, _, constrs)), 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

744 
(_, (_, _, constrs'))), tname), T), T'), constr_syntax)) = 
17870  745 
let 
746 
val rep_const = cterm_of thy 

747 
(Const (Sign.intern_const thy ("Rep_" ^ tname), T > T')); 

748 
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); 

749 
val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T') 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

750 
((Theory.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax) 
17870  751 
in 
752 
(parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) 

753 
end; 

754 

755 
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs 

756 
((thy7, [], [], []), List.take (descr, length new_type_names) ~~ 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

757 
List.take (pdescr, length new_type_names) ~~ 
17870  758 
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax); 
759 

760 
val abs_inject_thms = map (fn tname => 

761 
PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names; 

762 

763 
val rep_inject_thms = map (fn tname => 

764 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names; 

765 

766 
val rep_thms = map (fn tname => 

767 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names; 

768 

769 
val rep_inverse_thms = map (fn tname => 

770 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names; 

771 

772 
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) 

773 

774 
fun prove_constr_rep_thm eqn = 

775 
let 

776 
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; 

777 
val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms 

20046  778 
in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY 
17870  779 
[resolve_tac inj_thms 1, 
780 
rewrite_goals_tac rewrites, 

781 
rtac refl 3, 

782 
resolve_tac rep_intrs 2, 

20046  783 
REPEAT (resolve_tac rep_thms 1)]) 
17870  784 
end; 
785 

786 
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; 

787 

788 
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) 

789 

790 
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => 

791 
let 

792 
val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th); 

793 
val Type ("fun", [T, U]) = fastype_of Rep; 

794 
val permT = mk_permT (Type (atom, [])); 

795 
val pi = Free ("pi", permT); 

796 
in 

20046  797 
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
19494  798 
(Const ("Nominal.perm", permT > U > U) $ pi $ (Rep $ x), 
799 
Rep $ (Const ("Nominal.perm", permT > T > T) $ pi $ x)))) 

18010  800 
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ 
20046  801 
perm_closed_thms @ Rep_thms)) 1) 
17870  802 
end) Rep_thms; 
803 

804 
val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm 

805 
(atoms ~~ perm_closed_thmss)); 

806 

807 
(* prove distinctness theorems *) 

808 

18016  809 
val distinct_props = setmp DatatypeProp.dtK 1000 
810 
(DatatypeProp.make_distincts new_type_names descr' sorts') thy8; 

17870  811 

812 
val dist_rewrites = map (fn (rep_thms, dist_lemma) => 

813 
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) 

814 
(constr_rep_thmss ~~ dist_lemmas); 

815 

816 
fun prove_distinct_thms (_, []) = [] 

817 
 prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) = 

818 
let 

20046  819 
val dist_thm = Goal.prove_global thy8 [] [] t (fn _ => 
820 
simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1) 

17870  821 
in dist_thm::(standard (dist_thm RS not_sym)):: 
822 
(prove_distinct_thms (p, ts)) 

823 
end; 

824 

825 
val distinct_thms = map prove_distinct_thms 

826 
(constr_rep_thmss ~~ dist_lemmas ~~ distinct_props); 

827 

828 
(** prove equations for permutation functions **) 

829 

830 
val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *) 

831 

832 
val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

833 
let val T = nth_dtyp' i 
17870  834 
in List.concat (map (fn (atom, perm_closed_thms) => 
835 
map (fn ((cname, dts), constr_rep_thm) => 

836 
let 

837 
val cname = Sign.intern_const thy8 

838 
(NameSpace.append tname (Sign.base_name cname)); 

839 
val permT = mk_permT (Type (atom, [])); 

840 
val pi = Free ("pi", permT); 

841 

842 
fun perm t = 

843 
let val T = fastype_of t 

19494  844 
in Const ("Nominal.perm", permT > T > T) $ pi $ t end; 
17870  845 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

846 
fun constr_arg ((dts, dt), (j, l_args, r_args)) = 
17870  847 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

848 
val Ts = map (typ_of_dtyp descr'' sorts') dts; 
17870  849 
val xs = map (fn (T, i) => mk_Free "x" T i) 
850 
(Ts ~~ (j upto j + length dts  1)) 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

851 
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

852 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

853 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

854 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

855 
map perm (xs @ [x]) @ r_args) 
17870  856 
end 
857 

858 
val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts; 

859 
val c = Const (cname, map fastype_of l_args > T) 

860 
in 

20046  861 
Goal.prove_global thy8 [] [] 
17870  862 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
18010  863 
(perm (list_comb (c, l_args)), list_comb (c, r_args)))) 
864 
(fn _ => EVERY 

17870  865 
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, 
866 
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ 

867 
constr_defs @ perm_closed_thms)) 1, 

868 
TRY (simp_tac (HOL_basic_ss addsimps 

869 
(symmetric perm_fun_def :: abs_perm)) 1), 

870 
TRY (simp_tac (HOL_basic_ss addsimps 

871 
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ 

20046  872 
perm_closed_thms)) 1)]) 
17870  873 
end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss)) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

874 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  875 

876 
(** prove injectivity of constructors **) 

877 

878 
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; 

879 
val alpha = PureThy.get_thms thy8 (Name "alpha"); 

880 
val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh"); 

881 

882 
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

883 
let val T = nth_dtyp' i 
17870  884 
in List.mapPartial (fn ((cname, dts), constr_rep_thm) => 
885 
if null dts then NONE else SOME 

886 
let 

887 
val cname = Sign.intern_const thy8 

888 
(NameSpace.append tname (Sign.base_name cname)); 

889 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

890 
fun make_inj ((dts, dt), (j, args1, args2, eqs)) = 
17870  891 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

892 
val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts  1); 
17870  893 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 
894 
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx; 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

895 
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

896 
val y = mk_Free "y" (typ_of_dtyp descr'' sorts' dt) (j + length dts) 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

897 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

898 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

899 
xs @ (x :: args1), ys @ (y :: args2), 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

900 
HOLogic.mk_eq 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

901 
(foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs) 
17870  902 
end; 
903 

904 
val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts; 

905 
val Ts = map fastype_of args1; 

906 
val c = Const (cname, Ts > T) 

907 
in 

20046  908 
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
17870  909 
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), 
18010  910 
foldr1 HOLogic.mk_conj eqs))) 
911 
(fn _ => EVERY 

17870  912 
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: 
913 
rep_inject_thms')) 1, 

914 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: 

915 
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

916 
perm_rep_perm_thms)) 1), 
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset

917 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def :: 
20046  918 
expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]) 
17870  919 
end) (constrs ~~ constr_rep_thms) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

920 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  921 

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

922 
(** equations for support and freshness **) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

923 

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

924 
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

925 
(map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') => 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

926 
let val T = nth_dtyp' i 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

927 
in List.concat (map (fn (cname, dts) => map (fn atom => 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

928 
let 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

929 
val cname = Sign.intern_const thy8 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

930 
(NameSpace.append tname (Sign.base_name cname)); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

931 
val atomT = Type (atom, []); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

932 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

933 
fun process_constr ((dts, dt), (j, args1, args2)) = 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

934 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

935 
val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts  1); 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

936 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

937 
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

938 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

939 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

940 
xs @ (x :: args1), foldr mk_abs_fun x xs :: args2) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

941 
end; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

942 

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

943 
val (_, args1, args2) = foldr process_constr (1, [], []) dts; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

944 
val Ts = map fastype_of args1; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

945 
val c = list_comb (Const (cname, Ts > T), args1); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

946 
fun supp t = 
19494  947 
Const ("Nominal.supp", fastype_of t > HOLogic.mk_setT atomT) $ t; 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

948 
fun fresh t = 
19494  949 
Const ("Nominal.fresh", atomT > fastype_of t > HOLogic.boolT) $ 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

950 
Free ("a", atomT) $ t; 
20046  951 
val supp_thm = Goal.prove_global thy8 [] [] 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

952 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

953 
(supp c, 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

954 
if null dts then Const ("{}", HOLogic.mk_setT atomT) 
18010  955 
else foldr1 (HOLogic.mk_binop "op Un") (map supp args2)))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

956 
(fn _ => 
18010  957 
simp_tac (HOL_basic_ss addsimps (supp_def :: 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

958 
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

959 
symmetric empty_def :: Finites.emptyI :: simp_thms @ 
20046  960 
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

961 
in 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

962 
(supp_thm, 
20046  963 
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

964 
(fresh c, 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

965 
if null dts then HOLogic.true_const 
18010  966 
else foldr1 HOLogic.mk_conj (map fresh args2)))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

967 
(fn _ => 
20046  968 
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

969 
end) atoms) constrs) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

970 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps'))); 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

971 

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

972 
(**** weak induction theorem ****) 
18016  973 

974 
fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) = 

975 
let 

976 
val Rep_t = Const (List.nth (rep_names, i), T > U) $ 

977 
mk_Free "x" T i; 

978 

979 
val Abs_t = Const (List.nth (abs_names, i), U > T) 

980 

981 
in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t, 

982 
Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $ 

983 
(mk_Free "P" (T > HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], 

984 
concls @ [mk_Free "P" (T > HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) 

985 
end; 

986 

987 
val (indrule_lemma_prems, indrule_lemma_concls) = 

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

988 
Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs')); 
18016  989 

20046  990 
val indrule_lemma = Goal.prove_global thy8 [] [] 
18016  991 
(Logic.mk_implies 
992 
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), 

993 
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY 

994 
[REPEAT (etac conjE 1), 

995 
REPEAT (EVERY 

996 
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, 

20046  997 
etac mp 1, resolve_tac Rep_thms 1])]); 
18016  998 

999 
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); 

1000 
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else 

1001 
map (Free o apfst fst o dest_Var) Ps; 

1002 
val indrule_lemma' = cterm_instantiate 

1003 
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; 

1004 

19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

1005 
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms; 
18016  1006 

1007 
val dt_induct_prop = DatatypeProp.make_ind descr' sorts'; 

20046  1008 
val dt_induct = Goal.prove_global thy8 [] 
18016  1009 
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) 
1010 
(fn prems => EVERY 

1011 
[rtac indrule_lemma' 1, 

1012 
(DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1, 

1013 
EVERY (map (fn (prem, r) => (EVERY 

1014 
[REPEAT (eresolve_tac Abs_inverse_thms' 1), 

1015 
simp_tac (HOL_basic_ss addsimps [symmetric r]) 1, 

1016 
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) 

20046  1017 
(prems ~~ constr_defs))]); 
18016  1018 

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

1019 
val case_names_induct = mk_case_names_induct descr''; 
18016  1020 

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

1021 
(**** prove that new datatypes have finite support ****) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1022 

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

1023 
val _ = warning "proving finite support for the new datatype"; 
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset

1024 

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

1025 
val indnames = DatatypeProp.make_tnames recTs; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1026 

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

1027 
val abs_supp = PureThy.get_thms thy8 (Name "abs_supp"); 
18067  1028 
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

1029 

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

1030 
val finite_supp_thms = map (fn atom => 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1031 
let val atomT = Type (atom, []) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1032 
in map standard (List.take 
20046  1033 
(split_conj_thm (Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1034 
(foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem 
19494  1035 
(Const ("Nominal.supp", T > HOLogic.mk_setT atomT) $ Free (s, T), 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1036 
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

1037 
(indnames ~~ recTs)))) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1038 
(fn _ => indtac dt_induct indnames 1 THEN 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1039 
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps 
18067  1040 
(abs_supp @ supp_atm @ 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1041 
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

1042 
List.concat supp_thms))))), 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1043 
length new_type_names)) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1044 
end) atoms; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1045 

18759  1046 
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add]; 
18658  1047 

1048 
val (_, thy9) = thy8 > 

1049 
Theory.add_path big_name > 

1050 
PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] >> 

1051 
PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] > 

1052 
Theory.parent_path >> 

1053 
DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms >> 

1054 
DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss >> 

1055 
DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' >> 

1056 
DatatypeAux.store_thmss "inject" new_type_names inject_thms >> 

1057 
DatatypeAux.store_thmss "supp" new_type_names supp_thms >> 

1058 
DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms > 

1059 
fold (fn (atom, ths) => fn thy => 

1060 
let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom) 

19275  1061 
in fold (fn T => AxClass.prove_arity 
18658  1062 
(fst (dest_Type T), 
1063 
replicate (length sorts) [class], [class]) 

19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

1064 
(ClassPackage.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy 
18658  1065 
end) (atoms ~~ finite_supp_thms); 
1066 

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

1067 
(**** strong induction theorem ****) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1068 

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

1069 
val pnames = if length descr'' = 1 then ["P"] 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1070 
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

1071 
val ind_sort = if null dt_atomTs then HOLogic.typeS 
19649  1072 
else Sign.certify_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^ 
18658  1073 
Sign.base_name (fst (dest_Type T)))) dt_atomTs); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1074 
val fsT = TFree ("'n", ind_sort); 
18658  1075 
val fsT' = TFree ("'n", HOLogic.typeS); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1076 

18658  1077 
val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' > HOLogic.mk_setT T))) 
1078 
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs); 

1079 

1080 
fun make_pred fsT i T = 

18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset

1081 
Free (List.nth (pnames, i), fsT > T > HOLogic.boolT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1082 

19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1083 
fun mk_fresh1 xs [] = [] 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1084 
 mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1085 
(HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x)))) 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1086 
(filter (fn (_, U) => T = U) (rev xs)) @ 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1087 
mk_fresh1 (y :: xs) ys; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1088 

10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1089 
fun mk_fresh2 xss [] = [] 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1090 
 mk_fresh2 xss ((p as (ys, _)) :: yss) = List.concat (map (fn y as (_, T) => 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1091 
map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1092 
(Const ("Nominal.fresh", T > U > HOLogic.boolT) $ Free y $ Free x)) 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1093 
(rev xss @ yss)) ys) @ 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1094 
mk_fresh2 (p :: xss) yss; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1095 

18658  1096 
fun make_ind_prem fsT f k T ((cname, cargs), idxs) = 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1097 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1098 
val recs = List.filter is_rec_type cargs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1099 
val Ts = map (typ_of_dtyp descr'' sorts') cargs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1100 
val recTs' = map (typ_of_dtyp descr'' sorts') recs; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1101 
val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1102 
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

1103 
val frees = tnames ~~ Ts; 
19710  1104 
val frees' = partition_cargs idxs frees; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1105 
val z = (Name.variant tnames "z", fsT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1106 

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

1107 
fun mk_prem ((dt, s), T) = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1108 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1109 
val (Us, U) = strip_type T; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1110 
val l = length Us 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1111 
in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop 
18658  1112 
(make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l)) 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1113 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1114 

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

1115 
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1116 
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop 
19710  1117 
(f T (Free p) (Free z))) (List.concat (map fst frees')) @ 
1118 
mk_fresh1 [] (List.concat (map fst frees')) @ 

1119 
mk_fresh2 [] frees' 

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

1120 

18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset

1121 
in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems, 
18658  1122 
HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $ 
18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset

1123 
list_comb (Const (cname, Ts > T), map Free frees)))) 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1124 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1125 

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

1126 
val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
18658  1127 
map (make_ind_prem fsT (fn T => fn t => fn u => 
19494  1128 
Const ("Nominal.fresh", T > fsT > HOLogic.boolT) $ t $ u) i T) 
18658  1129 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1130 
val tnames = DatatypeProp.make_tnames recTs; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1131 
val zs = Name.variant_list tnames (replicate (length descr'') "z"); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1132 
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 
18658  1133 
(map (fn ((((i, _), T), tname), z) => 
1134 
make_pred fsT i T $ Free (z, fsT) $ Free (tname, T)) 

1135 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

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

1136 
val induct = Logic.list_implies (ind_prems, ind_concl); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1137 

18658  1138 
val ind_prems' = 
1139 
map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')], 

1140 
HOLogic.mk_Trueprop (HOLogic.mk_mem (f $ Free ("x", fsT'), 

1141 
Const ("Finite_Set.Finites", HOLogic.mk_setT (body_type T)))))) fresh_fs @ 

1142 
List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => 

1143 
map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $ 

1144 
HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T) 

1145 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); 

1146 
val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 

1147 
(map (fn ((((i, _), T), tname), z) => 

1148 
make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T)) 

1149 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

1150 
val induct' = Logic.list_implies (ind_prems', ind_concl'); 

1151 

1152 
fun mk_perm Ts (t, u) = 

1153 
let 

1154 
val T = fastype_of1 (Ts, t); 

1155 
val U = fastype_of1 (Ts, u) 

19494  1156 
in Const ("Nominal.perm", T > U > U) $ t $ u end; 
18658  1157 

1158 
val aux_ind_vars = 

1159 
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~ 

1160 
map mk_permT dt_atomTs) @ [("z", fsT')]; 

1161 
val aux_ind_Ts = rev (map snd aux_ind_vars); 

1162 
val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 

1163 
(map (fn (((i, _), T), tname) => 

1164 
HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $ 

1165 
foldr (mk_perm aux_ind_Ts) (Free (tname, T)) 

1166 
(map Bound (length dt_atomTs downto 1)))) 

1167 
(descr'' ~~ recTs ~~ tnames))); 

1168 

1169 
fun mk_ind_perm i k p l vs j = 

1170 
let 

1171 
val n = length vs; 

1172 
val Ts = map snd vs; 

1173 
val T = List.nth (Ts, i  j); 

1174 
val pT = NominalAtoms.mk_permT T 

1175 
in 

1176 
Const ("List.list.Cons", HOLogic.mk_prodT (T, T) > pT > pT) $ 

1177 
(HOLogic.pair_const T T $ Bound (l  j) $ foldr (mk_perm Ts) 

1178 
(Bound (i  j)) 

1179 
(map (mk_ind_perm i k p l vs) (j  1 downto 0) @ 

1180 
map Bound (n  k  1 downto n  k  p))) $ 

1181 
Const ("List.list.Nil", pT) 

1182 
end; 

1183 

19710  1184 
fun mk_fresh i i' j k p l is vs _ _ = 
18658  1185 
let 
1186 
val n = length vs; 

1187 
val Ts = map snd vs; 

1188 
val T = List.nth (Ts, n  i  1  j); 

1189 
val f = the (AList.lookup op = fresh_fs T); 

1190 
val U = List.nth (Ts, n  i'  1); 

1191 
val S = HOLogic.mk_setT T; 

19710  1192 
val prms' = map Bound (n  k downto n  k  p + 1); 
18658  1193 
val prms = map (mk_ind_perm (n  i) k p (n  l) (("a", T) :: vs)) 
19710  1194 
(j  1 downto 0) @ prms'; 
1195 
val bs = rev (List.mapPartial 

1196 
(fn ((_, T'), i) => if T = T' then SOME (Bound i) else NONE) 

1197 
(List.take (vs, n  k  p  1) ~~ (1 upto n  k  p  1))); 

1198 
val ts = map (fn i => 

1199 
Const ("Nominal.supp", List.nth (Ts, n  i  1) > S) $ 

1200 
foldr (mk_perm (T :: Ts)) (Bound (n  i)) prms') is 

18658  1201 
in 
1202 
HOLogic.mk_Trueprop (Const ("Ex", (T > HOLogic.boolT) > HOLogic.boolT) $ 

1203 
Abs ("a", T, HOLogic.Not $ 

1204 
(Const ("op :", T > S > HOLogic.boolT) $ Bound 0 $ 

19710  1205 
(foldr (fn (t, u) => Const ("insert", T > S > S) $ t $ u) 
1206 
(foldl (fn (t, u) => Const ("op Un", S > S > S) $ u $ t) 

1207 
(f $ Bound (n  k  p)) 

1208 
(Const ("Nominal.supp", U > S) $ 

1209 
foldr (mk_perm (T :: Ts)) (Bound (n  i')) prms :: ts)) 

1210 
(foldr (mk_perm (T :: Ts)) (Bound (n  i  j)) prms :: bs))))) 

18658  1211 
end; 
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1212 

18658  1213 
fun mk_fresh_constr is p vs _ concl = 
1214 
let 

1215 
val n = length vs; 

1216 
val Ts = map snd vs; 

1217 
val _ $ (_ $ _ $ t) = concl; 

1218 
val c = head_of t; 

1219 
val T = body_type (fastype_of c); 

1220 
val k = foldr op + 0 (map (fn (_, i) => i + 1) is); 

1221 
val ps = map Bound (n  k  1 downto n  k  p); 

1222 
val (_, _, ts, us) = foldl (fn ((_, i), (m, n, ts, us)) => 

1223 
(m  i  1, n  i, 

1224 
ts @ map Bound (n downto n  i + 1) @ 

1225 
[foldr (mk_perm Ts) (Bound (m  i)) 

1226 
(map (mk_ind_perm m k p n vs) (i  1 downto 0) @ ps)], 

1227 
us @ map (fn j => foldr (mk_perm Ts) (Bound j) ps) (m downto m  i))) 

1228 
(n  1, n  k  p  2, [], []) is 

1229 
in 

1230 
HOLogic.mk_Trueprop (HOLogic.eq_const T $ list_comb (c, ts) $ list_comb (c, us)) 

1231 
end; 

1232 

1233 
val abs_fun_finite_supp = PureThy.get_thm thy9 (Name "abs_fun_finite_supp"); 

1234 

1235 
val at_finite_select = PureThy.get_thm thy9 (Name "at_finite_select"); 

1236 

1237 
val induct_aux_lemmas = List.concat (map (fn Type (s, _) => 

1238 
[PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "_inst")), 

1239 
PureThy.get_thm thy9 (Name ("fs_" ^ Sign.base_name s ^ "1")), 

1240 
PureThy.get_thm thy9 (Name ("at_" ^ Sign.base_name s ^ "_inst"))]) dt_atomTs); 

1241 

1242 
val induct_aux_lemmas' = map (fn Type (s, _) => 

1243 
PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "2")) RS sym) dt_atomTs; 

1244 

19710  1245 
val fresh_aux = PureThy.get_thms thy9 (Name "fresh_aux"); 
1246 

1247 
(********************************************************************** 

1248 
The subgoals occurring in the proof of induct_aux have the 

1249 
following parameters: 

1250 

1251 
x_1 ... x_k p_1 ... p_m z b_1 ... b_n 

1252 

1253 
where 

1254 

1255 
x_i : constructor arguments (introduced by weak induction rule) 

1256 
p_i : permutations (one for each atom type in the data type) 

1257 
z : freshness context 

1258 
b_i : newly introduced names for binders (sufficiently fresh) 

1259 
***********************************************************************) 

1260 

1261 
val _ = warning "proving strong induction theorem ..."; 

1262 

20046  1263 
val induct_aux = Goal.prove_global thy9 [] ind_prems' ind_concl' 
18658  1264 
(fn prems => EVERY 
1265 
([mk_subgoal 1 (K (K (K aux_ind_concl))), 

1266 
indtac dt_induct tnames 1] @ 

1267 
List.concat (map (fn ((_, (_, _, constrs)), (_, constrs')) => 

1268 
List.concat (map (fn ((cname, cargs), is) => 

1269 
[simp_tac (HOL_basic_ss addsimps List.concat perm_simps') 1, 

1270 
REPEAT (rtac allI 1)] @ 

1271 
List.concat (map 

1272 
(fn ((_, 0), _) => [] 

1273 
 ((i, j), k) => List.concat (map (fn j' => 

1274 
let 

1275 
val DtType (tname, _) = List.nth (cargs, i + j'); 

1276 
val atom = Sign.base_name tname 

1277 
in 

1278 
[mk_subgoal 1 (mk_fresh i (i + j) j' 

1279 
(length cargs) (length dt_atomTs) 

19710  1280 
(length cargs + length dt_atomTs + 1 + i  k) 
1281 
(List.mapPartial (fn (i', j) => 

1282 
if i = i' then NONE else SOME (i' + j)) is)), 

18658  1283 
rtac at_finite_select 1, 
1284 
rtac (PureThy.get_thm thy9 (Name ("at_" ^ atom ^ "_inst"))) 1, 

1285 
asm_full_simp_tac (simpset_of thy9 addsimps 

1286 
[PureThy.get_thm thy9 (Name ("fs_" ^ atom ^ "1"))]) 1, 

1287 
resolve_tac prems 1, 

1288 
etac exE 1, 

1289 
asm_full_simp_tac (simpset_of thy9 addsimps 

1290 
[symmetric fresh_def]) 1] 

1291 
end) (0 upto j  1))) (is ~~ (0 upto length is  1))) @ 

1292 
(if exists (not o equal 0 o snd) is then 

1293 
[mk_subgoal 1 (mk_fresh_constr is (length dt_atomTs)), 

1294 
asm_full_simp_tac (simpset_of thy9 addsimps 

1295 
(List.concat inject_thms @ 

1296 
alpha @ abs_perm @ abs_fresh @ [abs_fun_finite_supp] @ 

1297 
induct_aux_lemmas)) 1, 

1298 
dtac sym 1, 

19710  1299 
asm_full_simp_tac (simpset_of thy9) 1, 
18658  1300 
REPEAT (etac conjE 1)] 
1301 
else 

1302 
[]) @ 

1303 
[(resolve_tac prems THEN_ALL_NEW 

19710  1304 
(atac ORELSE' 
1305 
SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of 

1306 
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => 

1307 
asm_simp_tac (simpset_of thy9 addsimps fresh_aux) i 

ee9c7fa80d21
Extended strong induction rule with additiona 