author  wenzelm 
Sun, 08 Mar 2009 17:26:14 +0100  
changeset 30364  577edc39b501 
parent 30345  76fd85bbf139 
child 30450  7655e6533209 
permissions  rwrr 
19494  1 
(* Title: HOL/Nominal/nominal_package.ML 
2 
Author: Stefan Berghofer and Christian Urban, TU Muenchen 

3 

4 
Nominal datatype package for Isabelle/HOL. 

5 
*) 

17870  6 

7 
signature NOMINAL_PACKAGE = 

8 
sig 

9 
val add_nominal_datatype : bool > string list > (string list * bstring * mixfix * 

18068  10 
(bstring * string list * mixfix) list) list > theory > theory 
22433
400fa18e951f
 Changed format of descriptor contained in nominal_datatype_info
berghofe
parents:
22311
diff
changeset

11 
type descr 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

12 
type nominal_datatype_info 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

13 
val get_nominal_datatypes : theory > nominal_datatype_info Symtab.table 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

14 
val get_nominal_datatype : theory > string > nominal_datatype_info option 
22311  15 
val mk_perm: typ list > term > term > term 
22529
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

16 
val perm_of_pair: term * term > term 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

17 
val mk_not_sym: thm list > thm list 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

18 
val perm_simproc: simproc 
25823  19 
val fresh_const: typ > typ > term 
28373  20 
val fresh_star_const: typ > typ > term 
17870  21 
end 
22 

18068  23 
structure NominalPackage : NOMINAL_PACKAGE = 
17870  24 
struct 
25 

22274  26 
val finite_emptyI = thm "finite.emptyI"; 
21669  27 
val finite_Diff = thm "finite_Diff"; 
28 
val finite_Un = thm "finite_Un"; 

29 
val Un_iff = thm "Un_iff"; 

30 
val In0_eq = thm "In0_eq"; 

31 
val In1_eq = thm "In1_eq"; 

32 
val In0_not_In1 = thm "In0_not_In1"; 

33 
val In1_not_In0 = thm "In1_not_In0"; 

34 
val Un_assoc = thm "Un_assoc"; 

35 
val Collect_disj_eq = thm "Collect_disj_eq"; 

36 
val empty_def = thm "empty_def"; 

24459
fd114392bca9
Got rid of large simpset in proof of characteristic equations
berghofe
parents:
24218
diff
changeset

37 
val empty_iff = thm "empty_iff"; 
21669  38 

17870  39 
open DatatypeAux; 
18068  40 
open NominalAtoms; 
17870  41 

18016  42 
(** FIXME: DatatypePackage should export this function **) 
43 

44 
local 

45 

46 
fun dt_recs (DtTFree _) = [] 

47 
 dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts) 

48 
 dt_recs (DtRec i) = [i]; 

49 

50 
fun dt_cases (descr: descr) (_, args, constrs) = 

51 
let 

30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

52 
fun the_bname i = Long_Name.base_name (#1 (valOf (AList.lookup (op =) descr i))); 
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset

53 
val bnames = map the_bname (distinct op = (List.concat (map dt_recs args))); 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

54 
in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end; 
18016  55 

56 

57 
fun induct_cases descr = 

58 
DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr))); 

59 

60 
fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i)); 

61 

62 
in 

63 

64 
fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); 

65 

66 
fun mk_case_names_exhausts descr new = 

67 
map (RuleCases.case_names o exhaust_cases descr o #1) 

68 
(List.filter (fn ((_, (name, _, _))) => name mem_string new) descr); 

69 

70 
end; 

71 

22846  72 
(* theory data *) 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

73 

22433
400fa18e951f
 Changed format of descriptor contained in nominal_datatype_info
berghofe
parents:
22311
diff
changeset

74 
type descr = (int * (string * dtyp list * (string * (dtyp list * dtyp) list) list)) list; 
400fa18e951f
 Changed format of descriptor contained in nominal_datatype_info
berghofe
parents:
22311
diff
changeset

75 

21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

76 
type nominal_datatype_info = 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

77 
{index : int, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

78 
descr : descr, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

79 
sorts : (string * sort) list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

80 
rec_names : string list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

81 
rec_rewrites : thm list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

82 
induction : thm, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

83 
distinct : thm list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

84 
inject : thm list}; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

85 

f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

86 
structure NominalDatatypesData = TheoryDataFun 
22846  87 
( 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

88 
type T = nominal_datatype_info Symtab.table; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

89 
val empty = Symtab.empty; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

90 
val copy = I; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

91 
val extend = I; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

92 
fun merge _ tabs : T = Symtab.merge (K true) tabs; 
22846  93 
); 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

94 

f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

95 
val get_nominal_datatypes = NominalDatatypesData.get; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

96 
val put_nominal_datatypes = NominalDatatypesData.put; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

97 
val map_nominal_datatypes = NominalDatatypesData.map; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

98 
val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes; 
22846  99 

21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

100 

f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

101 
(**** make datatype info ****) 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

102 

f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

103 
fun make_dt_info descr sorts induct reccomb_names rec_thms 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

104 
(((i, (_, (tname, _, _))), distinct), inject) = 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

105 
(tname, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

106 
{index = i, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

107 
descr = descr, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

108 
sorts = sorts, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

109 
rec_names = reccomb_names, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

110 
rec_rewrites = rec_thms, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

111 
induction = induct, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

112 
distinct = distinct, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

113 
inject = inject}); 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

114 

18016  115 
(*******************************) 
116 

17870  117 
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); 
118 

119 

18658  120 
(** simplification procedure for sorting permutations **) 
121 

122 
val dj_cp = thm "dj_cp"; 

123 

124 
fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]), 

125 
Type ("fun", [_, U])])) = (T, U); 

126 

19494  127 
fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u 
18658  128 
 permTs_of _ = []; 
129 

19494  130 
fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) = 
18658  131 
let 
132 
val (aT as Type (a, []), S) = dest_permT T; 

133 
val (bT as Type (b, []), _) = dest_permT U 

134 
in if aT mem permTs_of u andalso aT <> bT then 

135 
let 

28731  136 
val cp = cp_inst_of thy a b; 
137 
val dj = dj_thm_of thy b a; 

18658  138 
val dj_cp' = [cp, dj] MRS dj_cp; 
139 
val cert = SOME o cterm_of thy 

140 
in 

141 
SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)] 

142 
[cert t, cert r, cert s] dj_cp')) 

143 
end 

144 
else NONE 

145 
end 

146 
 perm_simproc' thy ss _ = NONE; 

147 

148 
val perm_simproc = 

25985  149 
Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc'; 
18658  150 

151 
val meta_spec = thm "meta_spec"; 

152 

18582
4f4cc426b440
provide projections of induct_weak, induct_unsafe;
wenzelm
parents:
18579
diff
changeset

153 
fun projections rule = 
19874  154 
ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule 
18582
4f4cc426b440
provide projections of induct_weak, induct_unsafe;
wenzelm
parents:
18579
diff
changeset

155 
> map (standard #> RuleCases.save rule); 
4f4cc426b440
provide projections of induct_weak, induct_unsafe;
wenzelm
parents:
18579
diff
changeset

156 

20267  157 
val supp_prod = thm "supp_prod"; 
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset

158 
val fresh_prod = thm "fresh_prod"; 
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset

159 
val supports_fresh = thm "supports_fresh"; 
22812  160 
val supports_def = thm "Nominal.supports_def"; 
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset

161 
val fresh_def = thm "fresh_def"; 
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset

162 
val supp_def = thm "supp_def"; 
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset

163 
val rev_simps = thms "rev.simps"; 
23029  164 
val app_simps = thms "append.simps"; 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

165 
val at_fin_set_supp = thm "at_fin_set_supp"; 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

166 
val at_fin_set_fresh = thm "at_fin_set_fresh"; 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

167 
val abs_fun_eq1 = thm "abs_fun_eq1"; 
20267  168 

21021  169 
val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; 
170 

22311  171 
fun mk_perm Ts t u = 
172 
let 

173 
val T = fastype_of1 (Ts, t); 

174 
val U = fastype_of1 (Ts, u) 

175 
in Const ("Nominal.perm", T > U > U) $ t $ u end; 

176 

22529
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

177 
fun perm_of_pair (x, y) = 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

178 
let 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

179 
val T = fastype_of x; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

180 
val pT = mk_permT T 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

181 
in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) > pT > pT) $ 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

182 
HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT) 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

183 
end; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

184 

902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

185 
fun mk_not_sym ths = maps (fn th => case prop_of th of 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

186 
_ $ (Const ("Not", _) $ (Const ("op =", _) $ _ $ _)) => [th, th RS not_sym] 
22529
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

187 
 _ => [th]) ths; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

188 

25823  189 
fun fresh_const T U = Const ("Nominal.fresh", T > U > HOLogic.boolT); 
28373  190 
fun fresh_star_const T U = 
191 
Const ("Nominal.fresh_star", HOLogic.mk_setT T > U > HOLogic.boolT); 

25823  192 

17870  193 
fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy = 
194 
let 

195 
(* this theory is used just for parsing *) 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

196 

17870  197 
val tmp_thy = thy > 
198 
Theory.copy > 

24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset

199 
Sign.add_types (map (fn (tvs, tname, mx, _) => 
30345  200 
(Binding.name tname, length tvs, mx)) dts); 
17870  201 

202 
val atoms = atoms_of thy; 

203 

204 
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) = 

22578  205 
let val (cargs', sorts') = Library.foldl (prep_typ tmp_thy) (([], sorts), cargs) 
17870  206 
in (constrs @ [(cname, cargs', mx)], sorts') end 
207 

208 
fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) = 

209 
let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs) 

210 
in (dts @ [(tvs, tname, mx, constrs')], sorts') end 

211 

212 
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts); 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

213 
val tyvars = map (map (fn s => 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

214 
(s, the (AList.lookup (op =) sorts s))) o #1) dts'; 
17870  215 

28731  216 
fun inter_sort thy S S' = Type.inter_sort (Sign.tsig_of thy) (S, S'); 
217 
fun augment_sort_typ thy S = 

218 
let val S = Sign.certify_sort thy S 

219 
in map_type_tfree (fn (s, S') => TFree (s, 

220 
if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S')) 

221 
end; 

222 
fun augment_sort thy S = map_types (augment_sort_typ thy S); 

223 

17870  224 
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts'; 
225 
val constr_syntax = map (fn (tvs, tname, mx, constrs) => 

226 
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; 

227 

228 
val ps = map (fn (_, n, _, _) => 

28965  229 
(Sign.full_bname tmp_thy n, Sign.full_bname tmp_thy (n ^ "_Rep"))) dts; 
17870  230 
val rps = map Library.swap ps; 
231 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

232 
fun replace_types (Type ("Nominal.ABS", [T, U])) = 
19494  233 
Type ("fun", [T, Type ("Nominal.noption", [replace_types U])]) 
17870  234 
 replace_types (Type (s, Ts)) = 
235 
Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts) 

236 
 replace_types T = T; 

237 

30345  238 
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, Binding.name (tname ^ "_Rep"), NoSyn, 
239 
map (fn (cname, cargs, mx) => (Binding.name (cname ^ "_Rep"), 

28731  240 
map replace_types cargs, NoSyn)) constrs)) dts'; 
17870  241 

242 
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; 

28965  243 
val full_new_type_names' = map (Sign.full_bname thy) new_type_names'; 
17870  244 

18045  245 
val ({induction, ...},thy1) = 
27112  246 
DatatypePackage.add_datatype err flat_names new_type_names' dts'' thy; 
17870  247 

248 
val SOME {descr, ...} = Symtab.lookup 

249 
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names'); 

28731  250 
fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

251 

26651  252 
val big_name = space_implode "_" new_type_names; 
253 

254 

17870  255 
(**** define permutation functions ****) 
256 

257 
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); 

258 
val pi = Free ("pi", permT); 

259 
val perm_types = map (fn (i, _) => 

260 
let val T = nth_dtyp i 

261 
in permT > T > T end) descr; 

26680  262 
val perm_names' = DatatypeProp.indexify_names (map (fn (i, _) => 
263 
"perm_" ^ name_of_typ (nth_dtyp i)) descr); 

19494  264 
val perm_names = replicate (length new_type_names) "Nominal.perm" @ 
28965  265 
map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names)); 
17870  266 
val perm_names_types = perm_names ~~ perm_types; 
26680  267 
val perm_names_types' = perm_names' ~~ perm_types; 
17870  268 

26680  269 
val perm_eqs = maps (fn (i, (_, _, constrs)) => 
17870  270 
let val T = nth_dtyp i 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

271 
in map (fn (cname, dts) => 
17870  272 
let 
28731  273 
val Ts = map (typ_of_dtyp descr sorts) dts; 
28641
f6e1b2beb766
Names of variables in perm_eqs are now chosen more carefully to avoid
berghofe
parents:
28373
diff
changeset

274 
val names = Name.variant_list ["pi"] (DatatypeProp.make_tnames Ts); 
17870  275 
val args = map Free (names ~~ Ts); 
276 
val c = Const (cname, Ts > T); 

277 
fun perm_arg (dt, x) = 

278 
let val T = type_of x 

279 
in if is_rec_type dt then 

280 
let val (Us, _) = strip_type T 

281 
in list_abs (map (pair "x") Us, 

26680  282 
Free (nth perm_names_types' (body_index dt)) $ pi $ 
17870  283 
list_comb (x, map (fn (i, U) => 
19494  284 
Const ("Nominal.perm", permT > U > U) $ 
17870  285 
(Const ("List.rev", permT > permT) $ pi) $ 
286 
Bound i) ((length Us  1 downto 0) ~~ Us))) 

287 
end 

19494  288 
else Const ("Nominal.perm", permT > T > T) $ pi $ x 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

289 
end; 
17870  290 
in 
28965  291 
(Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq 
26680  292 
(Free (nth perm_names_types' i) $ 
17870  293 
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ 
294 
list_comb (c, args), 

26680  295 
list_comb (c, map perm_arg (dts ~~ args))))) 
17870  296 
end) constrs 
26680  297 
end) descr; 
17870  298 

26689
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset

299 
val (perm_simps, thy2) = 
26680  300 
PrimrecPackage.add_primrec_overloaded 
26689
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset

301 
(map (fn (s, sT) => (s, sT, false)) 
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset

302 
(List.take (perm_names' ~~ perm_names_types, length new_type_names))) 
28965  303 
(map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1; 
17870  304 

305 
(**** prove that permutation functions introduced by unfolding are ****) 

306 
(**** equivalent to already existing permutation functions ****) 

307 

308 
val _ = warning ("length descr: " ^ string_of_int (length descr)); 

309 
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); 

310 

311 
val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types); 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

312 
val perm_fun_def = PureThy.get_thm thy2 "perm_fun_def"; 
17870  313 

314 
val unfolded_perm_eq_thms = 

315 
if length descr = length new_type_names then [] 

316 
else map standard (List.drop (split_conj_thm 

20046  317 
(Goal.prove_global thy2 [] [] 
17870  318 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
319 
(map (fn (c as (s, T), x) => 

320 
let val [T1, T2] = binder_types T 

321 
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), 

19494  322 
Const ("Nominal.perm", T) $ pi $ Free (x, T2)) 
17870  323 
end) 
18010  324 
(perm_names_types ~~ perm_indnames)))) 
325 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  326 
ALLGOALS (asm_full_simp_tac 
327 
(simpset_of thy2 addsimps [perm_fun_def]))])), 

328 
length new_type_names)); 

329 

330 
(**** prove [] \<bullet> t = t ****) 

331 

332 
val _ = warning "perm_empty_thms"; 

333 

334 
val perm_empty_thms = List.concat (map (fn a => 

335 
let val permT = mk_permT (Type (a, [])) 

336 
in map standard (List.take (split_conj_thm 

20046  337 
(Goal.prove_global thy2 [] [] 
28731  338 
(augment_sort thy2 [pt_class_of thy2 a] 
339 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

340 
(map (fn ((s, T), x) => HOLogic.mk_eq 

341 
(Const (s, permT > T > T) $ 

342 
Const ("List.list.Nil", permT) $ Free (x, T), 

343 
Free (x, T))) 

344 
(perm_names ~~ 

345 
map body_type perm_types ~~ perm_indnames))))) 

18010  346 
(fn _ => EVERY [indtac induction perm_indnames 1, 
17870  347 
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])), 
348 
length new_type_names)) 

349 
end) 

350 
atoms); 

351 

352 
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****) 

353 

354 
val _ = warning "perm_append_thms"; 

355 

356 
(*FIXME: these should be looked up statically*) 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

357 
val at_pt_inst = PureThy.get_thm thy2 "at_pt_inst"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

358 
val pt2 = PureThy.get_thm thy2 "pt2"; 
17870  359 

360 
val perm_append_thms = List.concat (map (fn a => 

361 
let 

362 
val permT = mk_permT (Type (a, [])); 

363 
val pi1 = Free ("pi1", permT); 

364 
val pi2 = Free ("pi2", permT); 

28731  365 
val pt_inst = pt_inst_of thy2 a; 
17870  366 
val pt2' = pt_inst RS pt2; 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

367 
val pt2_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a); 
17870  368 
in List.take (map standard (split_conj_thm 
20046  369 
(Goal.prove_global thy2 [] [] 
28731  370 
(augment_sort thy2 [pt_class_of thy2 a] 
17870  371 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
372 
(map (fn ((s, T), x) => 

373 
let val perm = Const (s, permT > T > T) 

374 
in HOLogic.mk_eq 

23029  375 
(perm $ (Const ("List.append", permT > permT > permT) $ 
17870  376 
pi1 $ pi2) $ Free (x, T), 
377 
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) 

378 
end) 

379 
(perm_names ~~ 

28731  380 
map body_type perm_types ~~ perm_indnames))))) 
18010  381 
(fn _ => EVERY [indtac induction perm_indnames 1, 
17870  382 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))), 
383 
length new_type_names) 

384 
end) atoms); 

385 

386 
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) 

387 

388 
val _ = warning "perm_eq_thms"; 

389 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

390 
val pt3 = PureThy.get_thm thy2 "pt3"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

391 
val pt3_rev = PureThy.get_thm thy2 "pt3_rev"; 
17870  392 

393 
val perm_eq_thms = List.concat (map (fn a => 

394 
let 

395 
val permT = mk_permT (Type (a, [])); 

396 
val pi1 = Free ("pi1", permT); 

397 
val pi2 = Free ("pi2", permT); 

28731  398 
val at_inst = at_inst_of thy2 a; 
399 
val pt_inst = pt_inst_of thy2 a; 

17870  400 
val pt3' = pt_inst RS pt3; 
401 
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); 

30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

402 
val pt3_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a); 
17870  403 
in List.take (map standard (split_conj_thm 
28731  404 
(Goal.prove_global thy2 [] [] 
405 
(augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies 

19494  406 
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq", 
17870  407 
permT > permT > HOLogic.boolT) $ pi1 $ pi2), 
408 
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

409 
(map (fn ((s, T), x) => 

410 
let val perm = Const (s, permT > T > T) 

411 
in HOLogic.mk_eq 

412 
(perm $ pi1 $ Free (x, T), 

413 
perm $ pi2 $ Free (x, T)) 

414 
end) 

415 
(perm_names ~~ 

28731  416 
map body_type perm_types ~~ perm_indnames)))))) 
18010  417 
(fn _ => EVERY [indtac induction perm_indnames 1, 
17870  418 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), 
419 
length new_type_names) 

420 
end) atoms); 

421 

422 
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) 

423 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

424 
val cp1 = PureThy.get_thm thy2 "cp1"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

425 
val dj_cp = PureThy.get_thm thy2 "dj_cp"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

426 
val pt_perm_compose = PureThy.get_thm thy2 "pt_perm_compose"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

427 
val pt_perm_compose_rev = PureThy.get_thm thy2 "pt_perm_compose_rev"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

428 
val dj_perm_perm_forget = PureThy.get_thm thy2 "dj_perm_perm_forget"; 
17870  429 

430 
fun composition_instance name1 name2 thy = 

431 
let 

28731  432 
val cp_class = cp_class_of thy name1 name2; 
433 
val pt_class = 

434 
if name1 = name2 then [pt_class_of thy name1] 

435 
else []; 

17870  436 
val permT1 = mk_permT (Type (name1, [])); 
437 
val permT2 = mk_permT (Type (name2, [])); 

28731  438 
val Ts = map body_type perm_types; 
439 
val cp_inst = cp_inst_of thy name1 name2; 

17870  440 
val simps = simpset_of thy addsimps (perm_fun_def :: 
441 
(if name1 <> name2 then 

28731  442 
let val dj = dj_thm_of thy name2 name1 
17870  443 
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end 
444 
else 

445 
let 

28731  446 
val at_inst = at_inst_of thy name1; 
447 
val pt_inst = pt_inst_of thy name1; 

17870  448 
in 
449 
[cp_inst RS cp1 RS sym, 

450 
at_inst RS (pt_inst RS pt_perm_compose) RS sym, 

451 
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] 

452 
end)) 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

453 
val sort = Sign.certify_sort thy (cp_class :: pt_class); 
20046  454 
val thms = split_conj_thm (Goal.prove_global thy [] [] 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

455 
(augment_sort thy sort 
17870  456 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
457 
(map (fn ((s, T), x) => 

458 
let 

459 
val pi1 = Free ("pi1", permT1); 

460 
val pi2 = Free ("pi2", permT2); 

461 
val perm1 = Const (s, permT1 > T > T); 

462 
val perm2 = Const (s, permT2 > T > T); 

19494  463 
val perm3 = Const ("Nominal.perm", permT1 > permT2 > permT2) 
17870  464 
in HOLogic.mk_eq 
465 
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), 

466 
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) 

467 
end) 

28731  468 
(perm_names ~~ Ts ~~ perm_indnames))))) 
18010  469 
(fn _ => EVERY [indtac induction perm_indnames 1, 
20046  470 
ALLGOALS (asm_full_simp_tac simps)])) 
17870  471 
in 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

472 
fold (fn (s, tvs) => fn thy => AxClass.prove_arity 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

473 
(s, map (inter_sort thy sort o snd) tvs, [cp_class]) 
24218  474 
(Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy) 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

475 
(full_new_type_names' ~~ tyvars) thy 
17870  476 
end; 
477 

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

478 
val (perm_thmss,thy3) = thy2 > 
17870  479 
fold (fn name1 => fold (composition_instance name1) atoms) atoms > 
28731  480 
fold (fn atom => fn thy => 
481 
let val pt_name = pt_class_of thy atom 

482 
in 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

483 
fold (fn (s, tvs) => fn thy => AxClass.prove_arity 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

484 
(s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name]) 
28731  485 
(EVERY 
486 
[Class.intro_classes_tac [], 

487 
resolve_tac perm_empty_thms 1, 

488 
resolve_tac perm_append_thms 1, 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

489 
resolve_tac perm_eq_thms 1, assume_tac 1]) thy) 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

490 
(full_new_type_names' ~~ tyvars) thy 
28731  491 
end) atoms > 
17870  492 
PureThy.add_thmss 
29585  493 
[((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"), 
18759  494 
unfolded_perm_eq_thms), [Simplifier.simp_add]), 
29585  495 
((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"), 
18759  496 
perm_empty_thms), [Simplifier.simp_add]), 
29585  497 
((Binding.name (space_implode "_" new_type_names ^ "_perm_append"), 
18759  498 
perm_append_thms), [Simplifier.simp_add]), 
29585  499 
((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"), 
18759  500 
perm_eq_thms), [Simplifier.simp_add])]; 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

501 

17870  502 
(**** Define representing sets ****) 
503 

504 
val _ = warning "representing sets"; 

505 

21021  506 
val rep_set_names = DatatypeProp.indexify_names 
507 
(map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr); 

17870  508 
val big_rep_name = 
509 
space_implode "_" (DatatypeProp.indexify_names (List.mapPartial 

19494  510 
(fn (i, ("Nominal.noption", _, _)) => NONE 
17870  511 
 (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set"; 
512 
val _ = warning ("big_rep_name: " ^ big_rep_name); 

513 

514 
fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) = 

515 
(case AList.lookup op = descr i of 

19494  516 
SOME ("Nominal.noption", _, [(_, [dt']), _]) => 
17870  517 
apfst (cons dt) (strip_option dt') 
518 
 _ => ([], dtf)) 

19494  519 
 strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) = 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

520 
apfst (cons dt) (strip_option dt') 
17870  521 
 strip_option dt = ([], dt); 
522 

28731  523 
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

524 
(List.concat (map (fn (_, (_, _, cs)) => List.concat 
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

525 
(map (List.concat o map (fst o strip_option) o snd) cs)) descr))); 
28731  526 
val dt_atoms = map (fst o dest_Type) dt_atomTs; 
18280
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

527 

17870  528 
fun make_intr s T (cname, cargs) = 
529 
let 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

530 
fun mk_prem (dt, (j, j', prems, ts)) = 
17870  531 
let 
532 
val (dts, dt') = strip_option dt; 

533 
val (dts', dt'') = strip_dtyp dt'; 

28731  534 
val Ts = map (typ_of_dtyp descr sorts) dts; 
535 
val Us = map (typ_of_dtyp descr sorts) dts'; 

536 
val T = typ_of_dtyp descr sorts dt''; 

17870  537 
val free = mk_Free "x" (Us > T) j; 
538 
val free' = app_bnds free (length Us); 

539 
fun mk_abs_fun (T, (i, t)) = 

540 
let val U = fastype_of t 

19494  541 
in (i + 1, Const ("Nominal.abs_fun", [T, U, T] > 
542 
Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t) 

17870  543 
end 
544 
in (j + 1, j' + length Ts, 

545 
case dt'' of 

546 
DtRec k => list_all (map (pair "x") Us, 

21021  547 
HOLogic.mk_Trueprop (Free (List.nth (rep_set_names, k), 
548 
T > HOLogic.boolT) $ free')) :: prems 

17870  549 
 _ => prems, 
30190  550 
snd (List.foldr mk_abs_fun (j', free) Ts) :: ts) 
17870  551 
end; 
552 

30190  553 
val (_, _, prems, ts) = List.foldr mk_prem (1, 1, [], []) cargs; 
21021  554 
val concl = HOLogic.mk_Trueprop (Free (s, T > HOLogic.boolT) $ 
555 
list_comb (Const (cname, map fastype_of ts > T), ts)) 

17870  556 
in Logic.list_implies (prems, concl) 
557 
end; 

558 

21021  559 
val (intr_ts, (rep_set_names', recTs')) = 
560 
apfst List.concat (apsnd ListPair.unzip (ListPair.unzip (List.mapPartial 

19494  561 
(fn ((_, ("Nominal.noption", _, _)), _) => NONE 
17870  562 
 ((i, (_, _, constrs)), rep_set_name) => 
563 
let val T = nth_dtyp i 

564 
in SOME (map (make_intr rep_set_name T) constrs, 

21021  565 
(rep_set_name, T)) 
17870  566 
end) 
21021  567 
(descr ~~ rep_set_names)))); 
28965  568 
val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names'; 
17870  569 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

570 
val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) = 
26475
3cc1e48d0ce1
eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents:
26359
diff
changeset

571 
InductivePackage.add_inductive_global (serial_string ()) 
3cc1e48d0ce1
eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents:
26359
diff
changeset

572 
{quiet_mode = false, verbose = false, kind = Thm.internalK, 
28965  573 
alt_name = Binding.name big_rep_name, coind = false, no_elim = true, no_ind = false, 
29389  574 
skip_mono = true, fork_mono = false} 
28965  575 
(map (fn (s, T) => ((Binding.name s, T > HOLogic.boolT), NoSyn)) 
26128  576 
(rep_set_names' ~~ recTs')) 
28965  577 
[] (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy3; 
17870  578 

579 
(**** Prove that representing set is closed under permutation ****) 

580 

581 
val _ = warning "proving closure under permutation..."; 

582 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

583 
val abs_perm = PureThy.get_thms thy4 "abs_perm"; 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

584 

17870  585 
val perm_indnames' = List.mapPartial 
19494  586 
(fn (x, (_, ("Nominal.noption", _, _))) => NONE  (x, _) => SOME x) 
17870  587 
(perm_indnames ~~ descr); 
588 

589 
fun mk_perm_closed name = map (fn th => standard (th RS mp)) 

20046  590 
(List.take (split_conj_thm (Goal.prove_global thy4 [] [] 
28731  591 
(augment_sort thy4 
592 
(pt_class_of thy4 name :: map (cp_class_of thy4 name) (dt_atoms \ name)) 

593 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map 

594 
(fn ((s, T), x) => 

595 
let 

596 
val S = Const (s, T > HOLogic.boolT); 

597 
val permT = mk_permT (Type (name, [])) 

598 
in HOLogic.mk_imp (S $ Free (x, T), 

599 
S $ (Const ("Nominal.perm", permT > T > T) $ 

600 
Free ("pi", permT) $ Free (x, T))) 

601 
end) (rep_set_names'' ~~ recTs' ~~ perm_indnames'))))) 

602 
(fn _ => EVERY 

17870  603 
[indtac rep_induct [] 1, 
604 
ALLGOALS (simp_tac (simpset_of thy4 addsimps 

25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

605 
(symmetric perm_fun_def :: abs_perm))), 
28731  606 
ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])), 
17870  607 
length new_type_names)); 
608 

609 
val perm_closed_thmss = map mk_perm_closed atoms; 

610 

611 
(**** typedef ****) 

612 

613 
val _ = warning "defining type..."; 

614 

18366  615 
val (typedefs, thy6) = 
26651  616 
thy4 
21021  617 
> fold_map (fn ((((name, mx), tvs), (cname, U)), name') => fn thy => 
30345  618 
TypedefPackage.add_typedef false (SOME (Binding.name name')) 
619 
(Binding.name name, map fst tvs, mx) 

21021  620 
(Const ("Collect", (U > HOLogic.boolT) > HOLogic.mk_setT U) $ 
621 
Const (cname, U > HOLogic.boolT)) NONE 

622 
(rtac exI 1 THEN rtac CollectI 1 THEN 

17870  623 
QUIET_BREADTH_FIRST (has_fewer_prems 1) 
26475
3cc1e48d0ce1
eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents:
26359
diff
changeset

624 
(resolve_tac rep_intrs 1)) thy > (fn ((_, r), thy) => 
17870  625 
let 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

626 
val permT = mk_permT 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

627 
(TFree (Name.variant (map fst tvs) "'a", HOLogic.typeS)); 
17870  628 
val pi = Free ("pi", permT); 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

629 
val T = Type (Sign.intern_type thy name, map TFree tvs); 
18366  630 
in apfst (pair r o hd) 
29585  631 
(PureThy.add_defs_unchecked true [((Binding.name ("prm_" ^ name ^ "_def"), Logic.mk_equals 
19494  632 
(Const ("Nominal.perm", permT > T > T) $ pi $ Free ("x", T), 
17870  633 
Const (Sign.intern_const thy ("Abs_" ^ name), U > T) $ 
19494  634 
(Const ("Nominal.perm", permT > U > U) $ pi $ 
17870  635 
(Const (Sign.intern_const thy ("Rep_" ^ name), T > U) $ 
636 
Free ("x", T))))), [])] thy) 

637 
end)) 

18366  638 
(types_syntax ~~ tyvars ~~ 
21021  639 
List.take (rep_set_names'' ~~ recTs', length new_type_names) ~~ 
640 
new_type_names); 

17870  641 

642 
val perm_defs = map snd typedefs; 

21021  643 
val Abs_inverse_thms = map (collect_simp o #Abs_inverse o fst) typedefs; 
18016  644 
val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs; 
21021  645 
val Rep_thms = map (collect_simp o #Rep o fst) typedefs; 
17870  646 

18016  647 

17870  648 
(** prove that new types are in class pt_<name> **) 
649 

650 
val _ = warning "prove that new types are in class pt_<name> ..."; 

651 

28731  652 
fun pt_instance (atom, perm_closed_thms) = 
21021  653 
fold (fn ((((((Abs_inverse, Rep_inverse), Rep), 
17870  654 
perm_def), name), tvs), perm_closed) => fn thy => 
28731  655 
let 
656 
val pt_class = pt_class_of thy atom; 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

657 
val sort = Sign.certify_sort thy 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

658 
(pt_class :: map (cp_class_of thy atom) (dt_atoms \ atom)) 
28731  659 
in AxClass.prove_arity 
17870  660 
(Sign.intern_type thy name, 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

661 
map (inter_sort thy sort o snd) tvs, [pt_class]) 
24218  662 
(EVERY [Class.intro_classes_tac [], 
17870  663 
rewrite_goals_tac [perm_def], 
664 
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1, 

665 
asm_full_simp_tac (simpset_of thy addsimps 

666 
[Rep RS perm_closed RS Abs_inverse]) 1, 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

667 
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

668 
("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy 
28731  669 
end) 
21021  670 
(Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ 
671 
new_type_names ~~ tyvars ~~ perm_closed_thms); 

17870  672 

673 

674 
(** prove that new types are in class cp_<name1>_<name2> **) 

675 

676 
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; 

677 

678 
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = 

679 
let 

28731  680 
val cp_class = cp_class_of thy atom1 atom2; 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

681 
val sort = Sign.certify_sort thy 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

682 
(pt_class_of thy atom1 :: map (cp_class_of thy atom1) (dt_atoms \ atom1) @ 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

683 
(if atom1 = atom2 then [cp_class_of thy atom1 atom1] else 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

684 
pt_class_of thy atom2 :: map (cp_class_of thy atom2) (dt_atoms \ atom2))); 
28731  685 
val cp1' = cp_inst_of thy atom1 atom2 RS cp1 
21021  686 
in fold (fn ((((((Abs_inverse, Rep), 
17870  687 
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => 
19275  688 
AxClass.prove_arity 
17870  689 
(Sign.intern_type thy name, 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

690 
map (inter_sort thy sort o snd) tvs, [cp_class]) 
24218  691 
(EVERY [Class.intro_classes_tac [], 
17870  692 
rewrite_goals_tac [perm_def], 
693 
asm_full_simp_tac (simpset_of thy addsimps 

694 
((Rep RS perm_closed1 RS Abs_inverse) :: 

695 
(if atom1 = atom2 then [] 

696 
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, 

18016  697 
cong_tac 1, 
17870  698 
rtac refl 1, 
699 
rtac cp1' 1]) thy) 

21021  700 
(Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~ 
701 
tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy 

17870  702 
end; 
703 

704 
val thy7 = fold (fn x => fn thy => thy > 

705 
pt_instance x > 

28731  706 
fold (cp_instance x) (atoms ~~ perm_closed_thmss)) 
707 
(atoms ~~ perm_closed_thmss) thy6; 

17870  708 

709 
(**** constructors ****) 

710 

711 
fun mk_abs_fun (x, t) = 

712 
let 

713 
val T = fastype_of x; 

714 
val U = fastype_of t 

715 
in 

19494  716 
Const ("Nominal.abs_fun", T > U > T > 
717 
Type ("Nominal.noption", [U])) $ x $ t 

17870  718 
end; 
719 

30190  720 
val (ty_idxs, _) = List.foldl 
19494  721 
(fn ((i, ("Nominal.noption", _, _)), p) => p 
18016  722 
 ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; 
723 

724 
fun reindex (DtType (s, dts)) = DtType (s, map reindex dts) 

725 
 reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i)) 

726 
 reindex dt = dt; 

727 

728 
fun strip_suffix i s = implode (List.take (explode s, size s  i)); 

729 

730 
(** strips the "_Rep" in type names *) 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

731 
fun strip_nth_name i s = 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

732 
let val xs = Long_Name.explode s; 
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

733 
in Long_Name.implode (Library.nth_map (length xs  i) (strip_suffix 4) xs) end; 
18016  734 

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

735 
val (descr'', ndescr) = ListPair.unzip (List.mapPartial 
19494  736 
(fn (i, ("Nominal.noption", _, _)) => NONE 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

737 
 (i, (s, dts, constrs)) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

738 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

739 
val SOME index = AList.lookup op = ty_idxs i; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

740 
val (constrs1, constrs2) = ListPair.unzip 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

741 
(map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname))) 
30190  742 
(Library.foldl_map (fn (dts, dt) => 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

743 
let val (dts', dt') = strip_option dt 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

744 
in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

745 
([], cargs))) constrs) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

746 
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

747 
(index, constrs2)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

748 
end) descr); 
18045  749 

19489  750 
val (descr1, descr2) = chop (length new_type_names) descr''; 
18016  751 
val descr' = [descr1, descr2]; 
752 

19710  753 
fun partition_cargs idxs xs = map (fn (i, j) => 
754 
(List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs; 

755 

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

756 
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

757 
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

758 
(constrs ~~ idxss)))) (descr'' ~~ ndescr); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

759 

28731  760 
fun nth_dtyp' i = typ_of_dtyp descr'' sorts (DtRec i); 
17870  761 

762 
val rep_names = map (fn s => 

763 
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; 

764 
val abs_names = map (fn s => 

765 
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; 

766 

28731  767 
val recTs = get_rec_types descr'' sorts; 
18016  768 
val newTs' = Library.take (length new_type_names, recTs'); 
769 
val newTs = Library.take (length new_type_names, recTs); 

17870  770 

28965  771 
val full_new_type_names = map (Sign.full_bname thy) new_type_names; 
17870  772 

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

773 
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

774 
(((cname_rep, _), (cname, cargs)), (cname', mx))) = 
17870  775 
let 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

776 
fun constr_arg ((dts, dt), (j, l_args, r_args)) = 
17870  777 
let 
28731  778 
val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts dt) i) 
17870  779 
(dts ~~ (j upto j + length dts  1)) 
28731  780 
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

781 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

782 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

783 
xs @ x :: l_args, 
30190  784 
List.foldr mk_abs_fun 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

785 
(case dt of 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

786 
DtRec k => if k < length new_type_names then 
28731  787 
Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts dt > 
788 
typ_of_dtyp descr sorts dt) $ x 

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

789 
else error "nested recursion not (yet) supported" 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

790 
 _ => x) xs :: r_args) 
17870  791 
end 
792 

30190  793 
val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs; 
22578  794 
val abs_name = Sign.intern_const thy ("Abs_" ^ tname); 
795 
val rep_name = Sign.intern_const thy ("Rep_" ^ tname); 

17870  796 
val constrT = map fastype_of l_args > T; 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

797 
val lhs = list_comb (Const (cname, constrT), l_args); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

798 
val rhs = list_comb (Const (cname_rep, map fastype_of r_args > T'), r_args); 
17870  799 
val def = Logic.mk_equals (lhs, Const (abs_name, T' > T) $ rhs); 
800 
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq 

801 
(Const (rep_name, T > T') $ lhs, rhs)); 

30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

802 
val def_name = (Long_Name.base_name cname) ^ "_def"; 
18366  803 
val ([def_thm], thy') = thy > 
30345  804 
Sign.add_consts_i [(Binding.name cname', constrT, mx)] > 
29585  805 
(PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)] 
17870  806 
in (thy', defs @ [def_thm], eqns @ [eqn]) end; 
807 

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

808 
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

809 
(_, (_, _, constrs'))), tname), T), T'), constr_syntax)) = 
17870  810 
let 
811 
val rep_const = cterm_of thy 

812 
(Const (Sign.intern_const thy ("Rep_" ^ tname), T > T')); 

813 
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); 

814 
val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T') 

24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset

815 
((Sign.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax) 
17870  816 
in 
817 
(parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) 

818 
end; 

819 

820 
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs 

821 
((thy7, [], [], []), List.take (descr, length new_type_names) ~~ 

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

822 
List.take (pdescr, length new_type_names) ~~ 
17870  823 
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax); 
824 

21021  825 
val abs_inject_thms = map (collect_simp o #Abs_inject o fst) typedefs 
826 
val rep_inject_thms = map (#Rep_inject o fst) typedefs 

17870  827 

828 
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) 

21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

829 

17870  830 
fun prove_constr_rep_thm eqn = 
831 
let 

832 
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; 

21021  833 
val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms 
20046  834 
in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY 
17870  835 
[resolve_tac inj_thms 1, 
836 
rewrite_goals_tac rewrites, 

837 
rtac refl 3, 

838 
resolve_tac rep_intrs 2, 

21021  839 
REPEAT (resolve_tac Rep_thms 1)]) 
17870  840 
end; 
841 

842 
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; 

843 

844 
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) 

845 

846 
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => 

847 
let 

21021  848 
val _ $ (_ $ (Rep $ x)) = Logic.unvarify (prop_of th); 
17870  849 
val Type ("fun", [T, U]) = fastype_of Rep; 
850 
val permT = mk_permT (Type (atom, [])); 

851 
val pi = Free ("pi", permT); 

852 
in 

28731  853 
Goal.prove_global thy8 [] [] 
854 
(augment_sort thy8 

855 
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom)) 

856 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

857 
(Const ("Nominal.perm", permT > U > U) $ pi $ (Rep $ x), 

858 
Rep $ (Const ("Nominal.perm", permT > T > T) $ pi $ x))))) 

18010  859 
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ 
20046  860 
perm_closed_thms @ Rep_thms)) 1) 
17870  861 
end) Rep_thms; 
862 

863 
val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm 

864 
(atoms ~~ perm_closed_thmss)); 

865 

866 
(* prove distinctness theorems *) 

867 

28731  868 
val distinct_props = DatatypeProp.make_distincts descr' sorts; 
27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

869 
val dist_rewrites = map2 (fn rep_thms => fn dist_lemma => 
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

870 
dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]) 
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

871 
constr_rep_thmss dist_lemmas; 
17870  872 

26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset

873 
fun prove_distinct_thms _ (_, []) = [] 
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset

874 
 prove_distinct_thms (p as (rep_thms, dist_lemma)) (k, t :: ts) = 
17870  875 
let 
20046  876 
val dist_thm = Goal.prove_global thy8 [] [] t (fn _ => 
877 
simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1) 

27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

878 
in dist_thm :: standard (dist_thm RS not_sym) :: 
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

879 
prove_distinct_thms p (k, ts) 
17870  880 
end; 
881 

26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset

882 
val distinct_thms = map2 prove_distinct_thms 
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset

883 
(constr_rep_thmss ~~ dist_lemmas) distinct_props; 
17870  884 

885 
(** prove equations for permutation functions **) 

886 

887 
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

888 
let val T = nth_dtyp' i 
17870  889 
in List.concat (map (fn (atom, perm_closed_thms) => 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

890 
map (fn ((cname, dts), constr_rep_thm) => 
17870  891 
let 
892 
val cname = Sign.intern_const thy8 

30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

893 
(Long_Name.append tname (Long_Name.base_name cname)); 
17870  894 
val permT = mk_permT (Type (atom, [])); 
895 
val pi = Free ("pi", permT); 

896 

897 
fun perm t = 

898 
let val T = fastype_of t 

19494  899 
in Const ("Nominal.perm", permT > T > T) $ pi $ t end; 
17870  900 

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

901 
fun constr_arg ((dts, dt), (j, l_args, r_args)) = 
17870  902 
let 
28731  903 
val Ts = map (typ_of_dtyp descr'' sorts) dts; 
17870  904 
val xs = map (fn (T, i) => mk_Free "x" T i) 
905 
(Ts ~~ (j upto j + length dts  1)) 

28731  906 
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

907 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

908 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

909 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

910 
map perm (xs @ [x]) @ r_args) 
17870  911 
end 
912 

30190  913 
val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) dts; 
17870  914 
val c = Const (cname, map fastype_of l_args > T) 
915 
in 

20046  916 
Goal.prove_global thy8 [] [] 
28731  917 
(augment_sort thy8 
918 
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom)) 

919 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

920 
(perm (list_comb (c, l_args)), list_comb (c, r_args))))) 

18010  921 
(fn _ => EVERY 
17870  922 
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, 
923 
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ 

924 
constr_defs @ perm_closed_thms)) 1, 

925 
TRY (simp_tac (HOL_basic_ss addsimps 

926 
(symmetric perm_fun_def :: abs_perm)) 1), 

927 
TRY (simp_tac (HOL_basic_ss addsimps 

928 
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ 

20046  929 
perm_closed_thms)) 1)]) 
17870  930 
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

931 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  932 

933 
(** prove injectivity of constructors **) 

934 

935 
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

936 
val alpha = PureThy.get_thms thy8 "alpha"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

937 
val abs_fresh = PureThy.get_thms thy8 "abs_fresh"; 
17870  938 

28731  939 
val pt_cp_sort = 
940 
map (pt_class_of thy8) dt_atoms @ 

941 
maps (fn s => map (cp_class_of thy8 s) (dt_atoms \ s)) dt_atoms; 

942 

17870  943 
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

944 
let val T = nth_dtyp' i 
17870  945 
in List.mapPartial (fn ((cname, dts), constr_rep_thm) => 
946 
if null dts then NONE else SOME 

947 
let 

948 
val cname = Sign.intern_const thy8 

30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

949 
(Long_Name.append tname (Long_Name.base_name cname)); 
17870  950 

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

951 
fun make_inj ((dts, dt), (j, args1, args2, eqs)) = 
17870  952 
let 
28731  953 
val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts  1); 
17870  954 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 
955 
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx; 

28731  956 
val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts); 
957 
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

958 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

959 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

960 
xs @ (x :: args1), ys @ (y :: args2), 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

961 
HOLogic.mk_eq 
30190  962 
(List.foldr mk_abs_fun x xs, List.foldr mk_abs_fun y ys) :: eqs) 
17870  963 
end; 
964 

30190  965 
val (_, args1, args2, eqs) = List.foldr make_inj (1, [], [], []) dts; 
17870  966 
val Ts = map fastype_of args1; 
967 
val c = Const (cname, Ts > T) 

968 
in 

28731  969 
Goal.prove_global thy8 [] [] 
970 
(augment_sort thy8 pt_cp_sort 

971 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

972 
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), 

973 
foldr1 HOLogic.mk_conj eqs)))) 

18010  974 
(fn _ => EVERY 
17870  975 
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: 
976 
rep_inject_thms')) 1, 

977 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: 

978 
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @ 

28731  979 
perm_rep_perm_thms)) 1)]) 
17870  980 
end) (constrs ~~ constr_rep_thms) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

981 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  982 

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

983 
(** equations for support and freshness **) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

984 

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

985 
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

986 
(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

987 
let val T = nth_dtyp' i 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

988 
in List.concat (map (fn (cname, dts) => map (fn atom => 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

989 
let 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

990 
val cname = Sign.intern_const thy8 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

991 
(Long_Name.append tname (Long_Name.base_name cname)); 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

992 
val atomT = Type (atom, []); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

993 

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

994 
fun process_constr ((dts, dt), (j, args1, args2)) = 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

995 
let 
28731  996 
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

997 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 
28731  998 
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

999 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

1000 
(j + length dts + 1, 
30190  1001 
xs @ (x :: args1), List.foldr mk_abs_fun x xs :: args2) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1002 
end; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1003 

30190  1004 
val (_, args1, args2) = List.foldr process_constr (1, [], []) dts; 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1005 
val Ts = map fastype_of args1; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1006 
val c = list_comb (Const (cname, Ts > T), args1); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1007 
fun supp t = 
19494  1008 
Const ("Nominal.supp", fastype_of t > HOLogic.mk_setT atomT) $ t; 
25823  1009 
fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t; 
20046  1010 
val supp_thm = Goal.prove_global thy8 [] [] 
28731  1011 
(augment_sort thy8 pt_cp_sort 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1012 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1013 
(supp c, 
30304
d8e4cd2ac2a1
set operations Int, Un, INTER, UNION, Inter, Union, empty, UNIV are now proper qualified constants with authentic syntax
haftmann
parents:
29585
diff
changeset

1014 
if null dts then Const (@{const_name Set.empty}, HOLogic.mk_setT atomT) 
d8e4cd2ac2a1
set operations Int, Un, INTER, UNION, Inter, Union, empty, UNIV are now proper qualified constants with authentic syntax
haftmann
parents:
29585
diff
changeset

1015 
else foldr1 (HOLogic.mk_binop @{const_name Un}) (map supp args2))))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1016 
(fn _ => 
18010  1017 
simp_tac (HOL_basic_ss addsimps (supp_def :: 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1018 
Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un :: 
22274  1019 
symmetric empty_def :: finite_emptyI :: simp_thms @ 
20046  1020 
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1021 
in 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1022 
(supp_thm, 
28731  1023 
Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort 
1024 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

1025 
(fresh c, 

1026 
if null dts then HOLogic.true_const 

1027 
else foldr1 HOLogic.mk_conj (map fresh args2))))) 

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

1028 
(fn _ => 
24459
fd114392bca9
Got rid of large simpset in proof of characteristic equations
berghofe
parents:
24218
diff
changeset

1029 
simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1)) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1030 
end) atoms) constrs) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

1031 
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

1032 

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

1033 
(**** weak induction theorem ****) 
18016  1034 

1035 
fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) = 

1036 
let 

1037 
val Rep_t = Const (List.nth (rep_names, i), T > U) $ 

1038 
mk_Free "x" T i; 

1039 

1040 
val Abs_t = Const (List.nth (abs_names, i), U > T) 

1041 

21021  1042 
in (prems @ [HOLogic.imp $ 
1043 
(Const (List.nth (rep_set_names'', i), U > HOLogic.boolT) $ Rep_t) $ 

18016  1044 
(mk_Free "P" (T > HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], 
1045 
concls @ [mk_Free "P" (T > HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) 

1046 
end; 

1047 

1048 
val (indrule_lemma_prems, indrule_lemma_concls) = 

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

1049 
Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs')); 
18016  1050 

20046  1051 
val indrule_lemma = Goal.prove_global thy8 [] [] 
18016  1052 
(Logic.mk_implies 
1053 
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), 

1054 
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY 

1055 
[REPEAT (etac conjE 1), 

1056 
REPEAT (EVERY 

1057 
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, 

20046  1058 
etac mp 1, resolve_tac Rep_thms 1])]); 
18016  1059 

1060 
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); 

1061 
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else 

1062 
map (Free o apfst fst o dest_Var) Ps; 

1063 
val indrule_lemma' = cterm_instantiate 

1064 
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; 

1065 

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

1066 
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms; 
18016  1067 

28731  1068 
val dt_induct_prop = DatatypeProp.make_ind descr' sorts; 
20046  1069 
val dt_induct = Goal.prove_global thy8 [] 
18016  1070 
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) 
26711  1071 
(fn {prems, ...} => EVERY 
18016  1072 
[rtac indrule_lemma' 1, 
25674  1073 
(indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, 
18016  1074 
EVERY (map (fn (prem, r) => (EVERY 
1075 
[REPEAT (eresolve_tac Abs_inverse_thms' 1), 

1076 
simp_tac (HOL_basic_ss addsimps [symmetric r]) 1, 

1077 
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) 

20046  1078 
(prems ~~ constr_defs))]); 
18016  1079 

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

1080 
val case_names_induct = mk_case_names_induct descr''; 
18016  1081 

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

1082 
(**** prove that new datatypes have finite support ****) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1083 

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

1084 
val _ = warning "proving finite support for the new datatype"; 
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset

1085 

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

1086 
val indnames = DatatypeProp.make_tnames recTs; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1087 

26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1088 
val abs_supp = PureThy.get_thms thy8 "abs_supp"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1089 
val supp_atm = PureThy.get_thms thy8 "supp_atm"; 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1090 

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

1091 
val finite_supp_thms = map (fn atom => 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1092 
let val atomT = Type (atom, []) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1093 
in map standard (List.take 
28731  1094 
(split_conj_thm (Goal.prove_global thy8 [] [] 
1095 
(augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort) 

1096 
(HOLogic.mk_Trueprop 

1097 
(foldr1 HOLogic.mk_conj (map (fn (s, T) => 

1098 
Const ("Finite_Set.finite", HOLogic.mk_setT atomT > HOLogic.boolT) $ 

1099 
(Const ("Nominal.supp", T > HOLogic.mk_setT atomT) $ Free (s, T))) 

1100 
(indnames ~~ recTs))))) 

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

1101 
(fn _ => indtac dt_induct indnames 1 THEN 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1102 
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps 
18067  1103 
(abs_supp @ supp_atm @ 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

1104 
PureThy.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @ 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1105 
List.concat supp_thms))))), 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1106 
length new_type_names)) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1107 
end) atoms; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1108 

18759  1109 
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add]; 
18658  1110 

22245
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1111 
(* Function to add both the simp and eqvt attributes *) 
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1112 
(* These two attributes are duplicated on all the types in the mutual nominal datatypes *) 
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1113 

1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1114 
val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add]; 
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1115 

18658  1116 
val (_, thy9) = thy8 > 
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset

1117 
Sign.add_path big_name > 
29585  1118 
PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] >> 
1119 
PureThy.add_thmss [((Binding.name "inducts", projections dt_induct), [case_names_induct])] > 

24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset

1120 
Sign.parent_path >> 
18658  1121 
DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms >> 
1122 
DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss >> 

22231
f76f187c91f9
added an infrastructure that allows the user to declare lemmas to be equivariance lemmas; the intention is to use these lemmas in automated tools but also can be employed by the user
urbanc
parents:
21858
diff
changeset

1123 
DatatypeAux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' >> 
18658  1124 
DatatypeAux.store_thmss "inject" new_type_names inject_thms >> 
1125 
DatatypeAux.store_thmss "supp" new_type_names supp_thms >> 

1126 
DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms > 

1127 
fold (fn (atom, ths) => fn thy => 

28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1128 
let 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1129 
val class = fs_class_of thy atom; 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1130 
val sort = Sign.certify_sort thy (class :: pt_cp_sort) 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1131 
in fold (fn Type (s, Ts) => AxClass.prove_arity 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1132 
(s, map (inter_sort thy sort o snd o dest_TFree) Ts, [class]) 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1133 
(Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy 
18658  1134 
end) (atoms ~~ finite_supp_thms); 
1135 

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

1136 
(**** strong induction theorem ****) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1137 

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

1138 
val pnames = if length descr'' = 1 then ["P"] 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1139 
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

1140 
val ind_sort = if null dt_atomTs then HOLogic.typeS 
28731  1141 
else Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1142 
val fsT = TFree ("'n", ind_sort); 
18658  1143 
val fsT' = TFree ("'n", HOLogic.typeS); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1144 

18658  1145 
val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' > HOLogic.mk_setT T))) 
1146 
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs); 

1147 

1148 
fun make_pred fsT i T = 

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

1149 
Free (List.nth (pnames, i), fsT > T > HOLogic.boolT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1150 

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

1151 
fun mk_fresh1 xs [] = [] 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1152 
 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

1153 
(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

1154 
(filter (fn (_, U) => T = U) (rev xs)) @ 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1155 
mk_fresh1 (y :: xs) ys; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1156 

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

1157 
fun mk_fresh2 xss [] = [] 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1158 
 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

1159 
map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop 
25823  1160 
(fresh_const T U $ Free y $ Free x)) (rev xss @ yss)) ys) @ 
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1161 
mk_fresh2 (p :: xss) yss; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1162 

18658  1163 
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

1164 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1165 
val recs = List.filter is_rec_type cargs; 
28731  1166 
val Ts = map (typ_of_dtyp descr'' sorts) cargs; 
1167 
val recTs' = map (typ_of_dtyp descr'' sorts) recs; 

20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1168 
val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1169 
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

1170 
val frees = tnames ~~ Ts; 
19710  1171 
val frees' = partition_cargs idxs frees; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1172 
val z = (Name.variant tnames "z", fsT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1173 

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

1174 
fun mk_prem ((dt, s), T) = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1175 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1176 
val (Us, U) = strip_type T; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1177 
val l = length Us 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1178 
in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop 
18658  1179 
(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

1180 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1181 

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

1182 
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1183 
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop 
19710  1184 
(f T (Free p) (Free z))) (List.concat (map fst frees')) @ 
1185 
mk_fresh1 [] (List.concat (map fst frees')) @ 

1186 
mk_fresh2 [] frees' 

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

1187 

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

1188 
in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems, 
18658  1189 
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

1190 
list_comb (Const (cname, Ts > T), map Free frees)))) 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1191 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1192 

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

1193 
val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
18658  1194 
map (make_ind_prem fsT (fn T => fn t => fn u => 
25823  1195 
fresh_const T fsT $ t $ u) i T) 
18658  1196 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1197 
val tnames = DatatypeProp.make_tnames recTs; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1198 
val zs = Name.variant_list tnames (replicate (length descr'') "z"); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1199 
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 
18658  1200 
(map (fn ((((i, _), T), tname), z) => 
1201 
make_pred fsT i T $ Free (z, fsT) $ Free (tname, T)) 

1202 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

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

1203 
val induct = Logic.list_implies (ind_prems, ind_concl); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1204 

18658  1205 
val ind_prems' = 
1206 
map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')], 

26806  1207 
HOLogic.mk_Trueprop (Const ("Finite_Set.finite", 
1208 
(snd (split_last (binder_types T)) > HOLogic.boolT) > 

1209 
HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @ 

18658  1210 
List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
1211 
map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $ 

1212 
HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T) 

1213 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); 

1214 
val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 

1215 
(map (fn ((((i, _), T), tname), z) => 

1216 
make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T)) 

1217 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

1218 
val induct' = Logic.list_implies (ind_prems', ind_concl'); 

1219 

1220 
val aux_ind_vars = 

1221 
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~ 

1222 
map mk_permT dt_atomTs) @ [("z", fsT')]; 

1223 
val aux_ind_Ts = rev (map snd aux_ind_vars); 

1224 
val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 

1225 
(map (fn (((i, _), T), tname) => 

1226 
HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $ 

22311  1227 
fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1)) 
1228 
(Free (tname, T)))) 

18658  1229 
(descr'' ~~ recTs ~~ tnames))); 
1230 

28731  1231 
val fin_set_supp = map (fn s => 
1232 
at_inst_of thy9 s RS at_fin_set_supp) dt_atoms; 

1233 
val fin_set_fresh = map (fn s => 

1234 
at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms; 

25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1235 
val pt1_atoms = map (fn Type (s, _) => 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

1236 
PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "1")) dt_atomTs; 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1237 
val pt2_atoms = map (fn Type (s, _) => 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

1238 
PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs; 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1239 
val exists_fresh' = PureThy.get_thms thy9 "exists_fresh'"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1240 
val fs_atoms = PureThy.get_thms thy9 "fin_supp"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1241 
val abs_supp = PureThy.get_thms thy9 "abs_supp"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1242 
val perm_fresh_fresh = PureThy.get_thms thy9 "perm_fresh_fresh"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1243 
val calc_atm = PureThy.get_thms thy9 "calc_atm"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1244 
val fresh_atm = PureThy.get_thms thy9 "fresh_atm"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1245 
val fresh_left = PureThy.get_thms thy9 "fresh_left"; 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

1246 
val perm_swap = PureThy.get_thms thy9 "perm_swap"; 
18658  1247 

25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1248 
fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) = 
18658  1249 
let 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1250 
val p = foldr1 HOLogic.mk_prod (ts @ freshs1); 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1251 
val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1252 
(HOLogic.exists_const T $ Abs ("x", T, 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1253 
fresh_const T (fastype_of p) $ 