author  wenzelm 
Sat, 07 Apr 2012 16:41:59 +0200  
changeset 47389  e8552cba702d 
parent 46961  5c6955f487e5 
child 49170  03bee3a6a1b7 
permissions  rwrr 
31936  1 
(* Title: HOL/Nominal/nominal_datatype.ML 
19494  2 
Author: Stefan Berghofer and Christian Urban, TU Muenchen 
3 

4 
Nominal datatype package for Isabelle/HOL. 

5 
*) 

17870  6 

31936  7 
signature NOMINAL_DATATYPE = 
17870  8 
sig 
45863  9 
val nominal_datatype : Datatype.config > Datatype.spec list > theory > theory 
10 
val nominal_datatype_cmd : Datatype.config > Datatype.spec_cmd 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 

31936  23 
structure NominalDatatype : NOMINAL_DATATYPE = 
17870  24 
struct 
25 

39159  26 
val finite_emptyI = @{thm finite.emptyI}; 
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}; 

32129  36 
val Collect_False_empty = @{thm empty_def [THEN sym, THEN eq_reflection]}; 
39159  37 
val empty_iff = @{thm empty_iff}; 
21669  38 

18068  39 
open NominalAtoms; 
17870  40 

18016  41 

22846  42 
(* theory data *) 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

43 

45838  44 
type descr = 
45896  45 
(int * (string * Datatype.dtyp list * 
46 
(string * (Datatype.dtyp list * Datatype.dtyp) list) list)) list; 

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

47 

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

48 
type nominal_datatype_info = 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

49 
{index : int, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

50 
descr : descr, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

51 
rec_names : string list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

52 
rec_rewrites : thm list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

53 
induction : thm, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

54 
distinct : thm list, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

55 
inject : thm list}; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

56 

33522  57 
structure NominalDatatypesData = Theory_Data 
22846  58 
( 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

59 
type T = nominal_datatype_info Symtab.table; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

60 
val empty = Symtab.empty; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

61 
val extend = I; 
33522  62 
fun merge data = Symtab.merge (K true) data; 
22846  63 
); 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

64 

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

65 
val get_nominal_datatypes = NominalDatatypesData.get; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

66 
val put_nominal_datatypes = NominalDatatypesData.put; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

67 
val map_nominal_datatypes = NominalDatatypesData.map; 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

68 
val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes; 
22846  69 

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

70 

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

71 
(**** make datatype info ****) 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

72 

45822  73 
fun make_dt_info descr induct reccomb_names rec_thms 
33063  74 
(i, (((_, (tname, _, _)), distinct), inject)) = 
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

75 
(tname, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

76 
{index = i, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

77 
descr = descr, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

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

79 
rec_rewrites = rec_thms, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

80 
induction = induct, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

81 
distinct = distinct, 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

82 
inject = inject}); 
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset

83 

18016  84 
(*******************************) 
85 

45909  86 
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of Datatype.distinct_lemma); 
17870  87 

88 

18658  89 
(** simplification procedure for sorting permutations **) 
90 

39159  91 
val dj_cp = @{thm dj_cp}; 
18658  92 

37677  93 
fun dest_permT (Type ("fun", [Type ("List.list", [Type (@{type_name Product_Type.prod}, [T, _])]), 
18658  94 
Type ("fun", [_, U])])) = (T, U); 
95 

19494  96 
fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u 
18658  97 
 permTs_of _ = []; 
98 

19494  99 
fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) = 
18658  100 
let 
101 
val (aT as Type (a, []), S) = dest_permT T; 

102 
val (bT as Type (b, []), _) = dest_permT U 

36692
54b64d4ad524
farewell to oldstyle mem infixes  type inference in situations with mem_int and mem_string should provide enough information to resolve the type of (op =)
haftmann
parents:
36610
diff
changeset

103 
in if member (op =) (permTs_of u) aT andalso aT <> bT then 
18658  104 
let 
28731  105 
val cp = cp_inst_of thy a b; 
106 
val dj = dj_thm_of thy b a; 

18658  107 
val dj_cp' = [cp, dj] MRS dj_cp; 
108 
val cert = SOME o cterm_of thy 

109 
in 

110 
SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)] 

111 
[cert t, cert r, cert s] dj_cp')) 

112 
end 

113 
else NONE 

114 
end 

115 
 perm_simproc' thy ss _ = NONE; 

116 

117 
val perm_simproc = 

38715
6513ea67d95d
renamed Simplifier.simproc(_i) to Simplifier.simproc_global(_i) to emphasize that this is not the real thing;
wenzelm
parents:
38558
diff
changeset

118 
Simplifier.simproc_global @{theory} "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc'; 
18658  119 

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

120 
fun projections rule = 
42361  121 
Project_Rule.projections (Proof_Context.init_global (Thm.theory_of_thm rule)) rule 
35021
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

122 
> map (Drule.export_without_context #> Rule_Cases.save rule); 
18582
4f4cc426b440
provide projections of induct_weak, induct_unsafe;
wenzelm
parents:
18579
diff
changeset

123 

39159  124 
val supp_prod = @{thm supp_prod}; 
125 
val fresh_prod = @{thm fresh_prod}; 

126 
val supports_fresh = @{thm supports_fresh}; 

44685
f5bc7d9d0d74
assert Pure equations for theorem references; avoid dynamic reference to fact
haftmann
parents:
44241
diff
changeset

127 
val supports_def = Simpdata.mk_eq @{thm Nominal.supports_def}; 
f5bc7d9d0d74
assert Pure equations for theorem references; avoid dynamic reference to fact
haftmann
parents:
44241
diff
changeset

128 
val fresh_def = Simpdata.mk_eq @{thm fresh_def}; 
f5bc7d9d0d74
assert Pure equations for theorem references; avoid dynamic reference to fact
haftmann
parents:
44241
diff
changeset

129 
val supp_def = Simpdata.mk_eq @{thm supp_def}; 
39159  130 
val rev_simps = @{thms rev.simps}; 
131 
val app_simps = @{thms append.simps}; 

132 
val at_fin_set_supp = @{thm at_fin_set_supp}; 

133 
val at_fin_set_fresh = @{thm at_fin_set_fresh}; 

134 
val abs_fun_eq1 = @{thm abs_fun_eq1}; 

20267  135 

21021  136 
val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; 
137 

22311  138 
fun mk_perm Ts t u = 
139 
let 

140 
val T = fastype_of1 (Ts, t); 

141 
val U = fastype_of1 (Ts, u) 

142 
in Const ("Nominal.perm", T > U > U) $ t $ u end; 

143 

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

144 
fun perm_of_pair (x, y) = 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

145 
let 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

146 
val T = fastype_of x; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

147 
val pT = mk_permT T 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

148 
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

149 
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

150 
end; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

151 

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

152 
fun mk_not_sym ths = maps (fn th => case prop_of th of 
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38795
diff
changeset

153 
_ $ (Const (@{const_name Not}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) => [th, th RS not_sym] 
22529
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

154 
 _ => [th]) ths; 
902ed60d53a7
Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
parents:
22433
diff
changeset

155 

25823  156 
fun fresh_const T U = Const ("Nominal.fresh", T > U > HOLogic.boolT); 
28373  157 
fun fresh_star_const T U = 
158 
Const ("Nominal.fresh_star", HOLogic.mk_setT T > U > HOLogic.boolT); 

25823  159 

45863  160 
fun gen_nominal_datatype prep_specs config dts thy = 
17870  161 
let 
45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

162 
val new_type_names = map (fn ((tname, _, _), _) => Binding.name_of tname) dts; 
45701  163 

45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

164 
val (dts', _) = prep_specs dts thy; 
17870  165 

166 
val atoms = atoms_of thy; 

167 

45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

168 
val tyvars = map (fn ((_, tvs, _), _) => tvs) dts'; 
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

169 
val sorts = flat tyvars; 
17870  170 

42388  171 
fun inter_sort thy S S' = Sign.inter_sort thy (S, S'); 
28731  172 
fun augment_sort_typ thy S = 
36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

173 
let val S = Sign.minimize_sort thy (Sign.certify_sort thy S) 
28731  174 
in map_type_tfree (fn (s, S') => TFree (s, 
175 
if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S')) 

176 
end; 

177 
fun augment_sort thy S = map_types (augment_sort_typ thy S); 

178 

45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

179 
val types_syntax = map (fn ((tname, tvs, mx), constrs) => (tname, mx)) dts'; 
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

180 
val constr_syntax = map (fn (_, constrs) => 
17870  181 
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; 
182 

45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

183 
val ps = map (fn ((n, _, _), _) => 
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

184 
(Sign.full_name thy n, Sign.full_name thy (Binding.suffix_name "_Rep" n))) dts; 
17870  185 
val rps = map Library.swap ps; 
186 

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

187 
fun replace_types (Type ("Nominal.ABS", [T, U])) = 
19494  188 
Type ("fun", [T, Type ("Nominal.noption", [replace_types U])]) 
17870  189 
 replace_types (Type (s, Ts)) = 
33035  190 
Type (the_default s (AList.lookup op = ps s), map replace_types Ts) 
17870  191 
 replace_types T = T; 
192 

45839
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

193 
val dts'' = map (fn ((tname, tvs, mx), constrs) => 
43a5b86bc102
'datatype' specifications allow explicit sort constraints;
wenzelm
parents:
45838
diff
changeset

194 
((Binding.suffix_name "_Rep" tname, tvs, NoSyn), 
45701  195 
map (fn (cname, cargs, mx) => (Binding.suffix_name "_Rep" cname, 
196 
map replace_types cargs, NoSyn)) constrs)) dts'; 

17870  197 

198 
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; 

199 

45701  200 
val (full_new_type_names',thy1) = Datatype.add_datatype config dts'' thy; 
17870  201 

45701  202 
val {descr, induct, ...} = Datatype.the_info thy1 (hd full_new_type_names'); 
45896  203 
fun nth_dtyp i = Datatype_Aux.typ_of_dtyp descr (Datatype.DtRec i); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

204 

26651  205 
val big_name = space_implode "_" new_type_names; 
206 

207 

17870  208 
(**** define permutation functions ****) 
209 

210 
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); 

211 
val pi = Free ("pi", permT); 

212 
val perm_types = map (fn (i, _) => 

213 
let val T = nth_dtyp i 

214 
in permT > T > T end) descr; 

33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

215 
val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) => 
45838  216 
"perm_" ^ Datatype_Aux.name_of_typ (nth_dtyp i)) descr); 
19494  217 
val perm_names = replicate (length new_type_names) "Nominal.perm" @ 
28965  218 
map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names)); 
17870  219 
val perm_names_types = perm_names ~~ perm_types; 
26680  220 
val perm_names_types' = perm_names' ~~ perm_types; 
17870  221 

26680  222 
val perm_eqs = maps (fn (i, (_, _, constrs)) => 
17870  223 
let val T = nth_dtyp i 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

224 
in map (fn (cname, dts) => 
17870  225 
let 
45838  226 
val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts; 
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

227 
val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts); 
17870  228 
val args = map Free (names ~~ Ts); 
229 
val c = Const (cname, Ts > T); 

230 
fun perm_arg (dt, x) = 

231 
let val T = type_of x 

45838  232 
in if Datatype_Aux.is_rec_type dt then 
40844  233 
let val Us = binder_types T 
46219
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

234 
in 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

235 
fold_rev (Term.abs o pair "x") Us 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

236 
(Free (nth perm_names_types' (Datatype_Aux.body_index dt)) $ pi $ 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

237 
list_comb (x, map (fn (i, U) => 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

238 
Const ("Nominal.perm", permT > U > U) $ 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

239 
(Const ("List.rev", permT > permT) $ pi) $ 
426ed18eba43
discontinued oldstyle Term.list_abs in favour of plain Term.abs;
wenzelm
parents:
46218
diff
changeset

240 
Bound i) ((length Us  1 downto 0) ~~ Us))) 
17870  241 
end 
19494  242 
else Const ("Nominal.perm", permT > T > T) $ pi $ x 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

243 
end; 
17870  244 
in 
28965  245 
(Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq 
26680  246 
(Free (nth perm_names_types' i) $ 
17870  247 
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ 
248 
list_comb (c, args), 

26680  249 
list_comb (c, map perm_arg (dts ~~ args))))) 
17870  250 
end) constrs 
26680  251 
end) descr; 
17870  252 

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

253 
val (perm_simps, thy2) = 
31723
f5cafe803b55
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents:
31671
diff
changeset

254 
Primrec.add_primrec_overloaded 
26689
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset

255 
(map (fn (s, sT) => (s, sT, false)) 
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset

256 
(List.take (perm_names' ~~ perm_names_types, length new_type_names))) 
28965  257 
(map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1; 
17870  258 

259 
(**** prove that permutation functions introduced by unfolding are ****) 

260 
(**** equivalent to already existing permutation functions ****) 

261 

262 
val _ = warning ("length descr: " ^ string_of_int (length descr)); 

263 
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); 

264 

33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

265 
val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); 
44685
f5bc7d9d0d74
assert Pure equations for theorem references; avoid dynamic reference to fact
haftmann
parents:
44241
diff
changeset

266 
val perm_fun_def = Simpdata.mk_eq @{thm perm_fun_def}; 
17870  267 

268 
val unfolded_perm_eq_thms = 

269 
if length descr = length new_type_names then [] 

45838  270 
else map Drule.export_without_context (List.drop (Datatype_Aux.split_conj_thm 
20046  271 
(Goal.prove_global thy2 [] [] 
17870  272 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
273 
(map (fn (c as (s, T), x) => 

274 
let val [T1, T2] = binder_types T 

275 
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), 

19494  276 
Const ("Nominal.perm", T) $ pi $ Free (x, T2)) 
17870  277 
end) 
18010  278 
(perm_names_types ~~ perm_indnames)))) 
45735  279 
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, 
17870  280 
ALLGOALS (asm_full_simp_tac 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

281 
(global_simpset_of thy2 addsimps [perm_fun_def]))])), 
17870  282 
length new_type_names)); 
283 

284 
(**** prove [] \<bullet> t = t ****) 

285 

286 
val _ = warning "perm_empty_thms"; 

287 

32952  288 
val perm_empty_thms = maps (fn a => 
17870  289 
let val permT = mk_permT (Type (a, [])) 
45838  290 
in map Drule.export_without_context (List.take (Datatype_Aux.split_conj_thm 
20046  291 
(Goal.prove_global thy2 [] [] 
28731  292 
(augment_sort thy2 [pt_class_of thy2 a] 
293 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

294 
(map (fn ((s, T), x) => HOLogic.mk_eq 

295 
(Const (s, permT > T > T) $ 

296 
Const ("List.list.Nil", permT) $ Free (x, T), 

297 
Free (x, T))) 

298 
(perm_names ~~ 

299 
map body_type perm_types ~~ perm_indnames))))) 

45735  300 
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

301 
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2))])), 
17870  302 
length new_type_names)) 
303 
end) 

32952  304 
atoms; 
17870  305 

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

307 

308 
val _ = warning "perm_append_thms"; 

309 

310 
(*FIXME: these should be looked up statically*) 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

311 
val at_pt_inst = Global_Theory.get_thm thy2 "at_pt_inst"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

312 
val pt2 = Global_Theory.get_thm thy2 "pt2"; 
17870  313 

32952  314 
val perm_append_thms = maps (fn a => 
17870  315 
let 
316 
val permT = mk_permT (Type (a, [])); 

317 
val pi1 = Free ("pi1", permT); 

318 
val pi2 = Free ("pi2", permT); 

28731  319 
val pt_inst = pt_inst_of thy2 a; 
17870  320 
val pt2' = pt_inst RS pt2; 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

321 
val pt2_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a); 
45838  322 
in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm 
20046  323 
(Goal.prove_global thy2 [] [] 
28731  324 
(augment_sort thy2 [pt_class_of thy2 a] 
17870  325 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
326 
(map (fn ((s, T), x) => 

327 
let val perm = Const (s, permT > T > T) 

328 
in HOLogic.mk_eq 

23029  329 
(perm $ (Const ("List.append", permT > permT > permT) $ 
17870  330 
pi1 $ pi2) $ Free (x, T), 
331 
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) 

332 
end) 

333 
(perm_names ~~ 

28731  334 
map body_type perm_types ~~ perm_indnames))))) 
45735  335 
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

336 
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt2', pt2_ax]))]))), 
17870  337 
length new_type_names) 
32952  338 
end) atoms; 
17870  339 

340 
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) 

341 

342 
val _ = warning "perm_eq_thms"; 

343 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

344 
val pt3 = Global_Theory.get_thm thy2 "pt3"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

345 
val pt3_rev = Global_Theory.get_thm thy2 "pt3_rev"; 
17870  346 

32952  347 
val perm_eq_thms = maps (fn a => 
17870  348 
let 
349 
val permT = mk_permT (Type (a, [])); 

350 
val pi1 = Free ("pi1", permT); 

351 
val pi2 = Free ("pi2", permT); 

28731  352 
val at_inst = at_inst_of thy2 a; 
353 
val pt_inst = pt_inst_of thy2 a; 

17870  354 
val pt3' = pt_inst RS pt3; 
355 
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

356 
val pt3_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a); 
45838  357 
in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm 
28731  358 
(Goal.prove_global thy2 [] [] 
359 
(augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies 

19494  360 
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq", 
17870  361 
permT > permT > HOLogic.boolT) $ pi1 $ pi2), 
362 
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

363 
(map (fn ((s, T), x) => 

364 
let val perm = Const (s, permT > T > T) 

365 
in HOLogic.mk_eq 

366 
(perm $ pi1 $ Free (x, T), 

367 
perm $ pi2 $ Free (x, T)) 

368 
end) 

369 
(perm_names ~~ 

28731  370 
map body_type perm_types ~~ perm_indnames)))))) 
45735  371 
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

372 
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), 
17870  373 
length new_type_names) 
32952  374 
end) atoms; 
17870  375 

376 
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) 

377 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

378 
val cp1 = Global_Theory.get_thm thy2 "cp1"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

379 
val dj_cp = Global_Theory.get_thm thy2 "dj_cp"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

380 
val pt_perm_compose = Global_Theory.get_thm thy2 "pt_perm_compose"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

381 
val pt_perm_compose_rev = Global_Theory.get_thm thy2 "pt_perm_compose_rev"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

382 
val dj_perm_perm_forget = Global_Theory.get_thm thy2 "dj_perm_perm_forget"; 
17870  383 

384 
fun composition_instance name1 name2 thy = 

385 
let 

28731  386 
val cp_class = cp_class_of thy name1 name2; 
387 
val pt_class = 

388 
if name1 = name2 then [pt_class_of thy name1] 

389 
else []; 

17870  390 
val permT1 = mk_permT (Type (name1, [])); 
391 
val permT2 = mk_permT (Type (name2, [])); 

28731  392 
val Ts = map body_type perm_types; 
393 
val cp_inst = cp_inst_of thy name1 name2; 

32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

394 
val simps = global_simpset_of thy addsimps (perm_fun_def :: 
17870  395 
(if name1 <> name2 then 
28731  396 
let val dj = dj_thm_of thy name2 name1 
17870  397 
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end 
398 
else 

399 
let 

28731  400 
val at_inst = at_inst_of thy name1; 
401 
val pt_inst = pt_inst_of thy name1; 

17870  402 
in 
403 
[cp_inst RS cp1 RS sym, 

404 
at_inst RS (pt_inst RS pt_perm_compose) RS sym, 

405 
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] 

406 
end)) 

36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

407 
val sort = Sign.minimize_sort thy (Sign.certify_sort thy (cp_class :: pt_class)); 
45838  408 
val thms = Datatype_Aux.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

409 
(augment_sort thy sort 
17870  410 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
411 
(map (fn ((s, T), x) => 

412 
let 

413 
val pi1 = Free ("pi1", permT1); 

414 
val pi2 = Free ("pi2", permT2); 

415 
val perm1 = Const (s, permT1 > T > T); 

416 
val perm2 = Const (s, permT2 > T > T); 

19494  417 
val perm3 = Const ("Nominal.perm", permT1 > permT2 > permT2) 
17870  418 
in HOLogic.mk_eq 
419 
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), 

420 
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) 

421 
end) 

28731  422 
(perm_names ~~ Ts ~~ perm_indnames))))) 
45735  423 
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, 
20046  424 
ALLGOALS (asm_full_simp_tac simps)])) 
17870  425 
in 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

426 
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

427 
(s, map (inter_sort thy sort o snd) tvs, [cp_class]) 
24218  428 
(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

429 
(full_new_type_names' ~~ tyvars) thy 
17870  430 
end; 
431 

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

432 
val (perm_thmss,thy3) = thy2 > 
17870  433 
fold (fn name1 => fold (composition_instance name1) atoms) atoms > 
28731  434 
fold (fn atom => fn thy => 
435 
let val pt_name = pt_class_of thy atom 

436 
in 

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

437 
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

438 
(s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name]) 
28731  439 
(EVERY 
440 
[Class.intro_classes_tac [], 

441 
resolve_tac perm_empty_thms 1, 

442 
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

443 
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

444 
(full_new_type_names' ~~ tyvars) thy 
28731  445 
end) atoms > 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

446 
Global_Theory.add_thmss 
29585  447 
[((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"), 
18759  448 
unfolded_perm_eq_thms), [Simplifier.simp_add]), 
29585  449 
((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"), 
18759  450 
perm_empty_thms), [Simplifier.simp_add]), 
29585  451 
((Binding.name (space_implode "_" new_type_names ^ "_perm_append"), 
18759  452 
perm_append_thms), [Simplifier.simp_add]), 
29585  453 
((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"), 
18759  454 
perm_eq_thms), [Simplifier.simp_add])]; 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

455 

17870  456 
(**** Define representing sets ****) 
457 

458 
val _ = warning "representing sets"; 

459 

45838  460 
val rep_set_names = 
461 
Datatype_Prop.indexify_names 

462 
(map (fn (i, _) => Datatype_Aux.name_of_typ (nth_dtyp i) ^ "_set") descr); 

17870  463 
val big_rep_name = 
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

464 
space_implode "_" (Datatype_Prop.indexify_names (map_filter 
19494  465 
(fn (i, ("Nominal.noption", _, _)) => NONE 
45838  466 
 (i, _) => SOME (Datatype_Aux.name_of_typ (nth_dtyp i))) descr)) ^ "_set"; 
17870  467 
val _ = warning ("big_rep_name: " ^ big_rep_name); 
468 

45896  469 
fun strip_option (dtf as Datatype.DtType ("fun", [dt, Datatype.DtRec i])) = 
17870  470 
(case AList.lookup op = descr i of 
19494  471 
SOME ("Nominal.noption", _, [(_, [dt']), _]) => 
17870  472 
apfst (cons dt) (strip_option dt') 
473 
 _ => ([], dtf)) 

45896  474 
 strip_option (Datatype.DtType ("fun", 
475 
[dt, Datatype.DtType ("Nominal.noption", [dt'])])) = 

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

476 
apfst (cons dt) (strip_option dt') 
17870  477 
 strip_option dt = ([], dt); 
478 

45838  479 
val dt_atomTs = distinct op = (map (Datatype_Aux.typ_of_dtyp descr) 
32952  480 
(maps (fn (_, (_, _, cs)) => maps (maps (fst o strip_option) o snd) cs) descr)); 
28731  481 
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

482 

17870  483 
fun make_intr s T (cname, cargs) = 
484 
let 

33338  485 
fun mk_prem dt (j, j', prems, ts) = 
17870  486 
let 
487 
val (dts, dt') = strip_option dt; 

45838  488 
val (dts', dt'') = Datatype_Aux.strip_dtyp dt'; 
489 
val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts; 

490 
val Us = map (Datatype_Aux.typ_of_dtyp descr) dts'; 

491 
val T = Datatype_Aux.typ_of_dtyp descr dt''; 

492 
val free = Datatype_Aux.mk_Free "x" (Us > T) j; 

493 
val free' = Datatype_Aux.app_bnds free (length Us); 

33338  494 
fun mk_abs_fun T (i, t) = 
17870  495 
let val U = fastype_of t 
19494  496 
in (i + 1, Const ("Nominal.abs_fun", [T, U, T] > 
45838  497 
Type ("Nominal.noption", [U])) $ Datatype_Aux.mk_Free "y" T i $ t) 
17870  498 
end 
499 
in (j + 1, j' + length Ts, 

500 
case dt'' of 

46218
ecf6375e2abb
renamed Term.list_all to Logic.list_all, in accordance to HOLogic.list_all;
wenzelm
parents:
46215
diff
changeset

501 
Datatype.DtRec k => Logic.list_all (map (pair "x") Us, 
42364  502 
HOLogic.mk_Trueprop (Free (nth rep_set_names k, 
21021  503 
T > HOLogic.boolT) $ free')) :: prems 
17870  504 
 _ => prems, 
33338  505 
snd (fold_rev mk_abs_fun Ts (j', free)) :: ts) 
17870  506 
end; 
507 

33338  508 
val (_, _, prems, ts) = fold_rev mk_prem cargs (1, 1, [], []); 
21021  509 
val concl = HOLogic.mk_Trueprop (Free (s, T > HOLogic.boolT) $ 
510 
list_comb (Const (cname, map fastype_of ts > T), ts)) 

17870  511 
in Logic.list_implies (prems, concl) 
512 
end; 

513 

21021  514 
val (intr_ts, (rep_set_names', recTs')) = 
32952  515 
apfst flat (apsnd ListPair.unzip (ListPair.unzip (map_filter 
19494  516 
(fn ((_, ("Nominal.noption", _, _)), _) => NONE 
17870  517 
 ((i, (_, _, constrs)), rep_set_name) => 
518 
let val T = nth_dtyp i 

519 
in SOME (map (make_intr rep_set_name T) constrs, 

21021  520 
(rep_set_name, T)) 
17870  521 
end) 
21021  522 
(descr ~~ rep_set_names)))); 
28965  523 
val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names'; 
17870  524 

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

525 
val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) = 
33278  526 
thy3 
527 
> Sign.map_naming Name_Space.conceal 

33726
0878aecbf119
eliminated slightly odd name space grouping  now managed by Isar toplevel;
wenzelm
parents:
33669
diff
changeset

528 
> Inductive.add_inductive_global 
33669  529 
{quiet_mode = false, verbose = false, alt_name = Binding.name big_rep_name, 
530 
coind = false, no_elim = true, no_ind = false, skip_mono = true, fork_mono = false} 

28965  531 
(map (fn (s, T) => ((Binding.name s, T > HOLogic.boolT), NoSyn)) 
26128  532 
(rep_set_names' ~~ recTs')) 
33278  533 
[] (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] 
534 
> Sign.restore_naming thy3; 

17870  535 

536 
(**** Prove that representing set is closed under permutation ****) 

537 

538 
val _ = warning "proving closure under permutation..."; 

539 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

540 
val abs_perm = Global_Theory.get_thms thy4 "abs_perm"; 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

541 

32952  542 
val perm_indnames' = map_filter 
19494  543 
(fn (x, (_, ("Nominal.noption", _, _))) => NONE  (x, _) => SOME x) 
17870  544 
(perm_indnames ~~ descr); 
545 

35021
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

546 
fun mk_perm_closed name = map (fn th => Drule.export_without_context (th RS mp)) 
45838  547 
(List.take (Datatype_Aux.split_conj_thm (Goal.prove_global thy4 [] [] 
28731  548 
(augment_sort thy4 
33040  549 
(pt_class_of thy4 name :: map (cp_class_of thy4 name) (remove (op =) name dt_atoms)) 
28731  550 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map 
551 
(fn ((s, T), x) => 

552 
let 

553 
val S = Const (s, T > HOLogic.boolT); 

554 
val permT = mk_permT (Type (name, [])) 

555 
in HOLogic.mk_imp (S $ Free (x, T), 

556 
S $ (Const ("Nominal.perm", permT > T > T) $ 

557 
Free ("pi", permT) $ Free (x, T))) 

558 
end) (rep_set_names'' ~~ recTs' ~~ perm_indnames'))))) 

559 
(fn _ => EVERY 

45735  560 
[Datatype_Aux.ind_tac rep_induct [] 1, 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

561 
ALLGOALS (simp_tac (global_simpset_of thy4 addsimps 
36945  562 
(Thm.symmetric perm_fun_def :: abs_perm))), 
28731  563 
ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])), 
17870  564 
length new_type_names)); 
565 

566 
val perm_closed_thmss = map mk_perm_closed atoms; 

567 

568 
(**** typedef ****) 

569 

570 
val _ = warning "defining type..."; 

571 

18366  572 
val (typedefs, thy6) = 
26651  573 
thy4 
45701  574 
> fold_map (fn (((name, mx), tvs), (cname, U)) => fn thy => 
575 
Typedef.add_typedef_global false NONE 

576 
(name, map (fn (v, _) => (v, dummyS)) tvs, mx) (* FIXME keep constraints!? *) 

37677  577 
(Const (@{const_name Collect}, (U > HOLogic.boolT) > HOLogic.mk_setT U) $ 
21021  578 
Const (cname, U > HOLogic.boolT)) NONE 
579 
(rtac exI 1 THEN rtac CollectI 1 THEN 

17870  580 
QUIET_BREADTH_FIRST (has_fewer_prems 1) 
26475
3cc1e48d0ce1
eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents:
26359
diff
changeset

581 
(resolve_tac rep_intrs 1)) thy > (fn ((_, r), thy) => 
17870  582 
let 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

583 
val permT = mk_permT 
43324
2b47822868e4
discontinued Name.variant to emphasize that this is oldstyle / indirect;
wenzelm
parents:
42388
diff
changeset

584 
(TFree (singleton (Name.variant_list (map fst tvs)) "'a", HOLogic.typeS)); 
17870  585 
val pi = Free ("pi", permT); 
45701  586 
val T = Type (Sign.full_name thy name, map TFree tvs); 
18366  587 
in apfst (pair r o hd) 
45701  588 
(Global_Theory.add_defs_unchecked true 
589 
[((Binding.map_name (fn n => "prm_" ^ n ^ "_def") name, Logic.mk_equals 

590 
(Const ("Nominal.perm", permT > T > T) $ pi $ Free ("x", T), 

591 
Const (Sign.intern_const thy ("Abs_" ^ Binding.name_of name), U > T) $ 

592 
(Const ("Nominal.perm", permT > U > U) $ pi $ 

593 
(Const (Sign.intern_const thy ("Rep_" ^ Binding.name_of name), T > U) $ 

594 
Free ("x", T))))), [])] thy) 

17870  595 
end)) 
45701  596 
(types_syntax ~~ tyvars ~~ List.take (rep_set_names'' ~~ recTs', length new_type_names)); 
17870  597 

598 
val perm_defs = map snd typedefs; 

35994
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset

599 
val Abs_inverse_thms = map (collect_simp o #Abs_inverse o snd o fst) typedefs; 
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset

600 
val Rep_inverse_thms = map (#Rep_inverse o snd o fst) typedefs; 
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset

601 
val Rep_thms = map (collect_simp o #Rep o snd o fst) typedefs; 
17870  602 

18016  603 

17870  604 
(** prove that new types are in class pt_<name> **) 
605 

606 
val _ = warning "prove that new types are in class pt_<name> ..."; 

607 

28731  608 
fun pt_instance (atom, perm_closed_thms) = 
21021  609 
fold (fn ((((((Abs_inverse, Rep_inverse), Rep), 
17870  610 
perm_def), name), tvs), perm_closed) => fn thy => 
28731  611 
let 
612 
val pt_class = pt_class_of thy atom; 

36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

613 
val sort = Sign.minimize_sort thy (Sign.certify_sort thy 
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

614 
(pt_class :: map (cp_class_of thy atom) (remove (op =) atom dt_atoms))) 
28731  615 
in AxClass.prove_arity 
17870  616 
(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

617 
map (inter_sort thy sort o snd) tvs, [pt_class]) 
24218  618 
(EVERY [Class.intro_classes_tac [], 
17870  619 
rewrite_goals_tac [perm_def], 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

620 
asm_full_simp_tac (global_simpset_of thy addsimps [Rep_inverse]) 1, 
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

621 
asm_full_simp_tac (global_simpset_of thy addsimps 
17870  622 
[Rep RS perm_closed RS Abs_inverse]) 1, 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

623 
asm_full_simp_tac (HOL_basic_ss addsimps [Global_Theory.get_thm thy 
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset

624 
("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy 
28731  625 
end) 
21021  626 
(Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ 
627 
new_type_names ~~ tyvars ~~ perm_closed_thms); 

17870  628 

629 

630 
(** prove that new types are in class cp_<name1>_<name2> **) 

631 

632 
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; 

633 

634 
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = 

635 
let 

28731  636 
val cp_class = cp_class_of thy atom1 atom2; 
36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

637 
val sort = Sign.minimize_sort thy (Sign.certify_sort thy 
33040  638 
(pt_class_of thy atom1 :: map (cp_class_of thy atom1) (remove (op =) atom1 dt_atoms) @ 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

639 
(if atom1 = atom2 then [cp_class_of thy atom1 atom1] else 
36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

640 
pt_class_of thy atom2 :: map (cp_class_of thy atom2) (remove (op =) atom2 dt_atoms)))); 
28731  641 
val cp1' = cp_inst_of thy atom1 atom2 RS cp1 
21021  642 
in fold (fn ((((((Abs_inverse, Rep), 
17870  643 
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => 
19275  644 
AxClass.prove_arity 
17870  645 
(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

646 
map (inter_sort thy sort o snd) tvs, [cp_class]) 
24218  647 
(EVERY [Class.intro_classes_tac [], 
17870  648 
rewrite_goals_tac [perm_def], 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

649 
asm_full_simp_tac (global_simpset_of thy addsimps 
17870  650 
((Rep RS perm_closed1 RS Abs_inverse) :: 
651 
(if atom1 = atom2 then [] 

652 
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, 

18016  653 
cong_tac 1, 
17870  654 
rtac refl 1, 
655 
rtac cp1' 1]) thy) 

21021  656 
(Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~ 
657 
tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy 

17870  658 
end; 
659 

660 
val thy7 = fold (fn x => fn thy => thy > 

661 
pt_instance x > 

28731  662 
fold (cp_instance x) (atoms ~~ perm_closed_thmss)) 
663 
(atoms ~~ perm_closed_thmss) thy6; 

17870  664 

665 
(**** constructors ****) 

666 

33338  667 
fun mk_abs_fun x t = 
17870  668 
let 
669 
val T = fastype_of x; 

670 
val U = fastype_of t 

671 
in 

19494  672 
Const ("Nominal.abs_fun", T > U > T > 
673 
Type ("Nominal.noption", [U])) $ x $ t 

17870  674 
end; 
675 

30190  676 
val (ty_idxs, _) = List.foldl 
19494  677 
(fn ((i, ("Nominal.noption", _, _)), p) => p 
18016  678 
 ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; 
679 

45896  680 
fun reindex (Datatype.DtType (s, dts)) = Datatype.DtType (s, map reindex dts) 
681 
 reindex (Datatype.DtRec i) = Datatype.DtRec (the (AList.lookup op = ty_idxs i)) 

18016  682 
 reindex dt = dt; 
683 

40627
becf5d5187cc
renamed raw "explode" function to "raw_explode" to emphasize its meaning;
wenzelm
parents:
39557
diff
changeset

684 
fun strip_suffix i s = implode (List.take (raw_explode s, size s  i)); (* FIXME Symbol.explode (?) *) 
18016  685 

686 
(** strips the "_Rep" in type names *) 

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

687 
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

688 
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

689 
in Long_Name.implode (Library.nth_map (length xs  i) (strip_suffix 4) xs) end; 
18016  690 

31458  691 
val (descr'', ndescr) = ListPair.unzip (map_filter 
19494  692 
(fn (i, ("Nominal.noption", _, _)) => NONE 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

693 
 (i, (s, dts, constrs)) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

694 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

695 
val SOME index = AList.lookup op = ty_idxs i; 
31458  696 
val (constrs2, constrs1) = 
697 
map_split (fn (cname, cargs) => 

698 
apsnd (pair (strip_nth_name 2 (strip_nth_name 1 cname))) 

699 
(fold_map (fn dt => fn dts => 

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

700 
let val (dts', dt') = strip_option dt 
31458  701 
in ((length dts, length dts'), dts @ dts' @ [reindex dt']) end) 
702 
cargs [])) constrs 

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

703 
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

704 
(index, constrs2)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

705 
end) descr); 
18045  706 

19489  707 
val (descr1, descr2) = chop (length new_type_names) descr''; 
18016  708 
val descr' = [descr1, descr2]; 
709 

19710  710 
fun partition_cargs idxs xs = map (fn (i, j) => 
42364  711 
(List.take (List.drop (xs, i), j), nth xs (i + j))) idxs; 
19710  712 

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

713 
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

714 
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

715 
(constrs ~~ idxss)))) (descr'' ~~ ndescr); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

716 

45896  717 
fun nth_dtyp' i = Datatype_Aux.typ_of_dtyp descr'' (Datatype.DtRec i); 
17870  718 

719 
val rep_names = map (fn s => 

720 
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; 

721 
val abs_names = map (fn s => 

722 
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; 

723 

45838  724 
val recTs = Datatype_Aux.get_rec_types descr''; 
33957  725 
val newTs' = take (length new_type_names) recTs'; 
726 
val newTs = take (length new_type_names) recTs; 

17870  727 

28965  728 
val full_new_type_names = map (Sign.full_bname thy) new_type_names; 
17870  729 

33244  730 
fun make_constr_def tname T T' (((cname_rep, _), (cname, cargs)), (cname', mx)) 
731 
(thy, defs, eqns) = 

17870  732 
let 
33338  733 
fun constr_arg (dts, dt) (j, l_args, r_args) = 
17870  734 
let 
45838  735 
val xs = 
736 
map (fn (dt, i) => Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) i) 

737 
(dts ~~ (j upto j + length dts  1)) 

738 
val x = Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts) 

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

739 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

740 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

741 
xs @ x :: l_args, 
33338  742 
fold_rev mk_abs_fun xs 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

743 
(case dt of 
45896  744 
Datatype.DtRec k => if k < length new_type_names then 
45838  745 
Const (nth rep_names k, Datatype_Aux.typ_of_dtyp descr'' dt > 
746 
Datatype_Aux.typ_of_dtyp descr dt) $ x 

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

747 
else error "nested recursion not (yet) supported" 
33338  748 
 _ => x) :: r_args) 
17870  749 
end 
750 

33338  751 
val (_, l_args, r_args) = fold_rev constr_arg cargs (1, [], []); 
22578  752 
val abs_name = Sign.intern_const thy ("Abs_" ^ tname); 
753 
val rep_name = Sign.intern_const thy ("Rep_" ^ tname); 

17870  754 
val constrT = map fastype_of l_args > T; 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

755 
val lhs = list_comb (Const (cname, constrT), l_args); 
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

756 
val rhs = list_comb (Const (cname_rep, map fastype_of r_args > T'), r_args); 
17870  757 
val def = Logic.mk_equals (lhs, Const (abs_name, T' > T) $ rhs); 
758 
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq 

759 
(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

760 
val def_name = (Long_Name.base_name cname) ^ "_def"; 
18366  761 
val ([def_thm], thy') = thy > 
45701  762 
Sign.add_consts_i [(cname', constrT, mx)] > 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

763 
(Global_Theory.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)] 
17870  764 
in (thy', defs @ [def_thm], eqns @ [eqn]) end; 
765 

33244  766 
fun dt_constr_defs ((((((_, (_, _, constrs)), 
767 
(_, (_, _, constrs'))), tname), T), T'), constr_syntax) (thy, defs, eqns, dist_lemmas) = 

17870  768 
let 
769 
val rep_const = cterm_of thy 

770 
(Const (Sign.intern_const thy ("Rep_" ^ tname), T > T')); 

33244  771 
val dist = 
35021
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

772 
Drule.export_without_context 
45909  773 
(cterm_instantiate [(cterm_of thy distinct_f, rep_const)] Datatype.distinct_lemma); 
33244  774 
val (thy', defs', eqns') = fold (make_constr_def tname T T') 
775 
(constrs ~~ constrs' ~~ constr_syntax) (Sign.add_path tname thy, defs, []) 

17870  776 
in 
32124  777 
(Sign.parent_path thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) 
17870  778 
end; 
779 

33244  780 
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = fold dt_constr_defs 
781 
(List.take (descr, length new_type_names) ~~ 

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

782 
List.take (pdescr, length new_type_names) ~~ 
33244  783 
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax) 
784 
(thy7, [], [], []); 

17870  785 

35994
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset

786 
val abs_inject_thms = map (collect_simp o #Abs_inject o snd o fst) typedefs 
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset

787 
val rep_inject_thms = map (#Rep_inject o snd o fst) typedefs 
17870  788 

789 
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) 

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

790 

17870  791 
fun prove_constr_rep_thm eqn = 
792 
let 

793 
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; 

21021  794 
val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms 
20046  795 
in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY 
17870  796 
[resolve_tac inj_thms 1, 
797 
rewrite_goals_tac rewrites, 

798 
rtac refl 3, 

799 
resolve_tac rep_intrs 2, 

21021  800 
REPEAT (resolve_tac Rep_thms 1)]) 
17870  801 
end; 
802 

803 
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; 

804 

805 
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) 

806 

807 
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => 

808 
let 

35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset

809 
val _ $ (_ $ (Rep $ x)) = Logic.unvarify_global (prop_of th); 
17870  810 
val Type ("fun", [T, U]) = fastype_of Rep; 
811 
val permT = mk_permT (Type (atom, [])); 

812 
val pi = Free ("pi", permT); 

813 
in 

28731  814 
Goal.prove_global thy8 [] [] 
815 
(augment_sort thy8 

33040  816 
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms)) 
28731  817 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
818 
(Const ("Nominal.perm", permT > U > U) $ pi $ (Rep $ x), 

819 
Rep $ (Const ("Nominal.perm", permT > T > T) $ pi $ x))))) 

18010  820 
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ 
20046  821 
perm_closed_thms @ Rep_thms)) 1) 
17870  822 
end) Rep_thms; 
823 

32952  824 
val perm_rep_perm_thms = maps prove_perm_rep_perm (atoms ~~ perm_closed_thmss); 
17870  825 

826 
(* prove distinctness theorems *) 

827 

45822  828 
val distinct_props = Datatype_Prop.make_distincts descr'; 
27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset

829 
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

830 
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

831 
constr_rep_thmss dist_lemmas; 
17870  832 

45889  833 
fun prove_distinct_thms _ [] = [] 
834 
 prove_distinct_thms (p as (rep_thms, dist_lemma)) (t :: ts) = 

17870  835 
let 
20046  836 
val dist_thm = Goal.prove_global thy8 [] [] t (fn _ => 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

837 
simp_tac (global_simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1) 
35021
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

838 
in 
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

839 
dist_thm :: Drule.export_without_context (dist_thm RS not_sym) :: 
45889  840 
prove_distinct_thms p ts 
17870  841 
end; 
842 

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

843 
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

844 
(constr_rep_thmss ~~ dist_lemmas) distinct_props; 
17870  845 

846 
(** prove equations for permutation functions **) 

847 

848 
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

849 
let val T = nth_dtyp' i 
32952  850 
in maps (fn (atom, perm_closed_thms) => 
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset

851 
map (fn ((cname, dts), constr_rep_thm) => 
17870  852 
let 
853 
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

854 
(Long_Name.append tname (Long_Name.base_name cname)); 
17870  855 
val permT = mk_permT (Type (atom, [])); 
856 
val pi = Free ("pi", permT); 

857 

858 
fun perm t = 

859 
let val T = fastype_of t 

19494  860 
in Const ("Nominal.perm", permT > T > T) $ pi $ t end; 
17870  861 

33338  862 
fun constr_arg (dts, dt) (j, l_args, r_args) = 
17870  863 
let 
45838  864 
val Ts = map (Datatype_Aux.typ_of_dtyp descr'') dts; 
865 
val xs = 

866 
map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) 

867 
(Ts ~~ (j upto j + length dts  1)); 

868 
val x = 

869 
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); 

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

870 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

871 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

872 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

873 
map perm (xs @ [x]) @ r_args) 
17870  874 
end 
875 

33338  876 
val (_, l_args, r_args) = fold_rev constr_arg dts (1, [], []); 
17870  877 
val c = Const (cname, map fastype_of l_args > T) 
878 
in 

20046  879 
Goal.prove_global thy8 [] [] 
28731  880 
(augment_sort thy8 
33040  881 
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms)) 
28731  882 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
883 
(perm (list_comb (c, l_args)), list_comb (c, r_args))))) 

18010  884 
(fn _ => EVERY 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

885 
[simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, 
17870  886 
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ 
887 
constr_defs @ perm_closed_thms)) 1, 

888 
TRY (simp_tac (HOL_basic_ss addsimps 

36945  889 
(Thm.symmetric perm_fun_def :: abs_perm)) 1), 
17870  890 
TRY (simp_tac (HOL_basic_ss addsimps 
891 
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ 

20046  892 
perm_closed_thms)) 1)]) 
32952  893 
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

894 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  895 

896 
(** prove injectivity of constructors **) 

897 

898 
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

899 
val alpha = Global_Theory.get_thms thy8 "alpha"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

900 
val abs_fresh = Global_Theory.get_thms thy8 "abs_fresh"; 
17870  901 

28731  902 
val pt_cp_sort = 
903 
map (pt_class_of thy8) dt_atoms @ 

33040  904 
maps (fn s => map (cp_class_of thy8 s) (remove (op =) s dt_atoms)) dt_atoms; 
28731  905 

17870  906 
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

907 
let val T = nth_dtyp' i 
32952  908 
in map_filter (fn ((cname, dts), constr_rep_thm) => 
17870  909 
if null dts then NONE else SOME 
910 
let 

911 
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

912 
(Long_Name.append tname (Long_Name.base_name cname)); 
17870  913 

33338  914 
fun make_inj (dts, dt) (j, args1, args2, eqs) = 
17870  915 
let 
45838  916 
val Ts_idx = 
917 
map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts  1); 

918 
val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx; 

919 
val ys = map (fn (T, i) => Datatype_Aux.mk_Free "y" T i) Ts_idx; 

920 
val x = 

921 
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); 

922 
val y = 

923 
Datatype_Aux.mk_Free "y" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); 

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

924 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

925 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

926 
xs @ (x :: args1), ys @ (y :: args2), 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

927 
HOLogic.mk_eq 
33338  928 
(fold_rev mk_abs_fun xs x, fold_rev mk_abs_fun ys y) :: eqs) 
17870  929 
end; 
930 

33338  931 
val (_, args1, args2, eqs) = fold_rev make_inj dts (1, [], [], []); 
17870  932 
val Ts = map fastype_of args1; 
933 
val c = Const (cname, Ts > T) 

934 
in 

28731  935 
Goal.prove_global thy8 [] [] 
936 
(augment_sort thy8 pt_cp_sort 

937 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

938 
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), 

939 
foldr1 HOLogic.mk_conj eqs)))) 

18010  940 
(fn _ => EVERY 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

941 
[asm_full_simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm :: 
17870  942 
rep_inject_thms')) 1, 
943 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: 

944 
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @ 

28731  945 
perm_rep_perm_thms)) 1)]) 
17870  946 
end) (constrs ~~ constr_rep_thms) 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

947 
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 
17870  948 

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

949 
(** equations for support and freshness **) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

950 

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

951 
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

952 
(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

953 
let val T = nth_dtyp' i 
32952  954 
in maps (fn (cname, dts) => map (fn atom => 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

955 
let 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

956 
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

957 
(Long_Name.append tname (Long_Name.base_name cname)); 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

958 
val atomT = Type (atom, []); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

959 

33338  960 
fun process_constr (dts, dt) (j, args1, args2) = 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

961 
let 
45838  962 
val Ts_idx = 
963 
map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts  1); 

964 
val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx; 

965 
val x = 

966 
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); 

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

967 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

968 
(j + length dts + 1, 
33338  969 
xs @ (x :: args1), fold_rev mk_abs_fun xs x :: args2) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

970 
end; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

971 

33338  972 
val (_, args1, args2) = fold_rev process_constr dts (1, [], []); 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

973 
val Ts = map fastype_of args1; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

974 
val c = list_comb (Const (cname, Ts > T), args1); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

975 
fun supp t = 
19494  976 
Const ("Nominal.supp", fastype_of t > HOLogic.mk_setT atomT) $ t; 
25823  977 
fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t; 
20046  978 
val supp_thm = Goal.prove_global thy8 [] [] 
28731  979 
(augment_sort thy8 pt_cp_sort 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

980 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

981 
(supp c, 
30450  982 
if null dts then HOLogic.mk_set atomT [] 
35402  983 
else foldr1 (HOLogic.mk_binop @{const_abbrev union}) (map supp args2))))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

984 
(fn _ => 
18010  985 
simp_tac (HOL_basic_ss addsimps (supp_def :: 
46161  986 
Un_assoc :: @{thm de_Morgan_conj} :: Collect_disj_eq :: finite_Un :: 
45654  987 
Collect_False_empty :: finite_emptyI :: @{thms simp_thms} @ 
20046  988 
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

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

990 
(supp_thm, 
28731  991 
Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort 
992 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 

993 
(fresh c, 

45740  994 
if null dts then @{term True} 
28731  995 
else foldr1 HOLogic.mk_conj (map fresh args2))))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

996 
(fn _ => 
24459
fd114392bca9
Got rid of large simpset in proof of characteristic equations
berghofe
parents:
24218
diff
changeset

997 
simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1)) 
32952  998 
end) atoms) constrs 
19833
3a3f591c838d
 Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset

999 
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

1000 

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

1001 
(**** weak induction theorem ****) 
18016  1002 

33244  1003 
fun mk_indrule_lemma (((i, _), T), U) (prems, concls) = 
18016  1004 
let 
45838  1005 
val Rep_t = Const (nth rep_names i, T > U) $ Datatype_Aux.mk_Free "x" T i; 
18016  1006 

42364  1007 
val Abs_t = Const (nth abs_names i, U > T); 
18016  1008 

45838  1009 
in 
1010 
(prems @ [HOLogic.imp $ 

42364  1011 
(Const (nth rep_set_names'' i, U > HOLogic.boolT) $ Rep_t) $ 
45838  1012 
(Datatype_Aux.mk_Free "P" (T > HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], 
1013 
concls @ 

1014 
[Datatype_Aux.mk_Free "P" (T > HOLogic.boolT) (i + 1) $ Datatype_Aux.mk_Free "x" T i]) 

18016  1015 
end; 
1016 

1017 
val (indrule_lemma_prems, indrule_lemma_concls) = 

33244  1018 
fold mk_indrule_lemma (descr'' ~~ recTs ~~ recTs') ([], []); 
18016  1019 

20046  1020 
val indrule_lemma = Goal.prove_global thy8 [] [] 
18016  1021 
(Logic.mk_implies 
45838  1022 
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems), 
1023 
HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls))) (fn _ => EVERY 

18016  1024 
[REPEAT (etac conjE 1), 
1025 
REPEAT (EVERY 

1026 
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, 

20046  1027 
etac mp 1, resolve_tac Rep_thms 1])]); 
18016  1028 

1029 
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); 

1030 
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else 

1031 
map (Free o apfst fst o dest_Var) Ps; 

1032 
val indrule_lemma' = cterm_instantiate 

1033 
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; 

1034 

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

1035 
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms; 
18016  1036 

45822  1037 
val dt_induct_prop = Datatype_Prop.make_ind descr'; 
20046  1038 
val dt_induct = Goal.prove_global thy8 [] 
18016  1039 
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) 
26711  1040 
(fn {prems, ...} => EVERY 
18016  1041 
[rtac indrule_lemma' 1, 
45735  1042 
(Datatype_Aux.ind_tac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1, 
18016  1043 
EVERY (map (fn (prem, r) => (EVERY 
1044 
[REPEAT (eresolve_tac Abs_inverse_thms' 1), 

36945  1045 
simp_tac (HOL_basic_ss addsimps [Thm.symmetric r]) 1, 
18016  1046 
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) 
20046  1047 
(prems ~~ constr_defs))]); 
18016  1048 

45906  1049 
val case_names_induct = Datatype.mk_case_names_induct descr''; 
18016  1050 

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

1051 
(**** prove that new datatypes have finite support ****) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1052 

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

1053 
val _ = warning "proving finite support for the new datatype"; 
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset

1054 

33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1055 
val indnames = Datatype_Prop.make_tnames recTs; 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1056 

39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1057 
val abs_supp = Global_Theory.get_thms thy8 "abs_supp"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1058 
val supp_atm = Global_Theory.get_thms thy8 "supp_atm"; 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1059 

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

1060 
val finite_supp_thms = map (fn atom => 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1061 
let val atomT = Type (atom, []) 
35021
c839a4c670c6
renamed oldstyle Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset

1062 
in map Drule.export_without_context (List.take 
45838  1063 
(Datatype_Aux.split_conj_thm (Goal.prove_global thy8 [] [] 
28731  1064 
(augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort) 
1065 
(HOLogic.mk_Trueprop 

1066 
(foldr1 HOLogic.mk_conj (map (fn (s, T) => 

1067 
Const ("Finite_Set.finite", HOLogic.mk_setT atomT > HOLogic.boolT) $ 

1068 
(Const ("Nominal.supp", T > HOLogic.mk_setT atomT) $ Free (s, T))) 

1069 
(indnames ~~ recTs))))) 

45735  1070 
(fn _ => Datatype_Aux.ind_tac dt_induct indnames 1 THEN 
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of  same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset

1071 
ALLGOALS (asm_full_simp_tac (global_simpset_of thy8 addsimps 
18067  1072 
(abs_supp @ supp_atm @ 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1073 
Global_Theory.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @ 
32952  1074 
flat supp_thms))))), 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1075 
length new_type_names)) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1076 
end) atoms; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1077 

18759  1078 
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add]; 
18658  1079 

32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32957
diff
changeset

1080 
(* Function to add both the simp and eqvt attributes *) 
22245
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset

1081 
(* 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

1082 

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

1083 
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

1084 

18658  1085 
val (_, thy9) = thy8 > 
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset

1086 
Sign.add_path big_name > 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1087 
Global_Theory.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] >> 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1088 
Global_Theory.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

1089 
Sign.parent_path >> 
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1090 
Datatype_Aux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms >> 
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1091 
Datatype_Aux.store_thmss "constr_rep" new_type_names constr_rep_thmss >> 
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1092 
Datatype_Aux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' >> 
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1093 
Datatype_Aux.store_thmss "inject" new_type_names inject_thms >> 
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1094 
Datatype_Aux.store_thmss "supp" new_type_names supp_thms >> 
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1095 
Datatype_Aux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms > 
18658  1096 
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

1097 
let 
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1098 
val class = fs_class_of thy atom; 
36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

1099 
val sort = Sign.minimize_sort thy (Sign.certify_sort thy (class :: pt_cp_sort)); 
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset

1100 
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

1101 
(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

1102 
(Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy 
18658  1103 
end) (atoms ~~ finite_supp_thms); 
1104 

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

1105 
(**** strong induction theorem ****) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1106 

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

1107 
val pnames = if length descr'' = 1 then ["P"] 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1108 
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

1109 
val ind_sort = if null dt_atomTs then HOLogic.typeS 
36428
874843c1e96e
really minimize sorts after certification  looks like this is intended here;
wenzelm
parents:
35994
diff
changeset

1110 
else Sign.minimize_sort thy9 (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

1111 
val fsT = TFree ("'n", ind_sort); 
18658  1112 
val fsT' = TFree ("'n", HOLogic.typeS); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1113 

18658  1114 
val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' > HOLogic.mk_setT T))) 
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1115 
(Datatype_Prop.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs); 
18658  1116 

42364  1117 
fun make_pred fsT i T = Free (nth pnames i, fsT > T > HOLogic.boolT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1118 

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

1119 
fun mk_fresh1 xs [] = [] 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1120 
 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

1121 
(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

1122 
(filter (fn (_, U) => T = U) (rev xs)) @ 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1123 
mk_fresh1 (y :: xs) ys; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1124 

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

1125 
fun mk_fresh2 xss [] = [] 
32952  1126 
 mk_fresh2 xss ((p as (ys, _)) :: yss) = maps (fn y as (_, T) => 
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1127 
map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop 
32952  1128 
(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

1129 
mk_fresh2 (p :: xss) yss; 
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset

1130 

18658  1131 
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

1132 
let 
45838  1133 
val recs = filter Datatype_Aux.is_rec_type cargs; 
1134 
val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs; 

1135 
val recTs' = map (Datatype_Aux.typ_of_dtyp descr'') recs; 

33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1136 
val tnames = Name.variant_list pnames (Datatype_Prop.make_tnames Ts); 
45838  1137 
val rec_tnames = map fst (filter (Datatype_Aux.is_rec_type o snd) (tnames ~~ cargs)); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1138 
val frees = tnames ~~ Ts; 
19710  1139 
val frees' = partition_cargs idxs frees; 
43324
2b47822868e4
discontinued Name.variant to emphasize that this is oldstyle / indirect;
wenzelm
parents:
42388
diff
changeset

1140 
val z = (singleton (Name.variant_list tnames) "z", fsT); 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1141 

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

1142 
fun mk_prem ((dt, s), T) = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1143 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1144 
val (Us, U) = strip_type T; 
45838  1145 
val l = length Us; 
1146 
in 

46218
ecf6375e2abb
renamed Term.list_all to Logic.list_all, in accordance to HOLogic.list_all;
wenzelm
parents:
46215
diff
changeset

1147 
Logic.list_all (z :: map (pair "x") Us, 
45838  1148 
HOLogic.mk_Trueprop 
1149 
(make_pred fsT (Datatype_Aux.body_index dt) U $ Bound l $ 

1150 
Datatype_Aux.app_bnds (Free (s, T)) l)) 

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

1151 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1152 

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

1153 
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1154 
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop 
32952  1155 
(f T (Free p) (Free z))) (maps fst frees') @ 
1156 
mk_fresh1 [] (maps fst frees') @ 

19710  1157 
mk_fresh2 [] frees' 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1158 

46215
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1159 
in 
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1160 
fold_rev (Logic.all o Free) (frees @ [z]) 
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1161 
(Logic.list_implies (prems' @ prems, 
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1162 
HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $ 
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1163 
list_comb (Const (cname, Ts > T), map Free frees)))) 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

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

1165 

32952  1166 
val ind_prems = maps (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
18658  1167 
map (make_ind_prem fsT (fn T => fn t => fn u => 
25823  1168 
fresh_const T fsT $ t $ u) i T) 
32952  1169 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs); 
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1170 
val tnames = Datatype_Prop.make_tnames recTs; 
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset

1171 
val zs = Name.variant_list tnames (replicate (length descr'') "z"); 
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset

1172 
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) 
18658  1173 
(map (fn ((((i, _), T), tname), z) => 
1174 
make_pred fsT i T $ Free (z, fsT) $ Free (tname, T)) 

1175 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

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

1176 
val induct = Logic.list_implies (ind_prems, ind_concl); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1177 

18658  1178 
val ind_prems' = 
46215
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1179 
map (fn (_, f as Free (_, T)) => Logic.all (Free ("x", fsT')) 
0da9433f959e
discontinued oldstyle Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset

1180 
(HOLogic.mk_Trueprop (Const ("Finite_Set.finite", 
44692
ccfc7c193d2b
modify nominal packages to better respect set/pred distinction
huffman
parents:
44241
diff
changeset

1181 
Term.range_type T > 
26806  1182 
HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @ 
32952  1183 
maps (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
18658  1184 
map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $ 
1185 
HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T) 

32952  1186 
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs); 
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset

1187 
val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) 
18658  1188 
(map (fn ((((i, _), T), tname), z) => 
1189 
make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T)) 

1190 
(descr'' ~~ recTs ~~ tnames ~~ zs))); 

1191 
val induct' = Logic.list_implies (ind_prems', ind_concl'); 

1192 

1193 
val aux_ind_vars = 

33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset

1194 
(Datatype_Prop.indexify_names (replicate (length dt_atomTs) "pi") ~~ 
18658  1195 
map mk_permT dt_atomTs) @ [("z", fsT')]; 
1196 
val aux_ind_Ts = rev (map snd aux_ind_vars); 

38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset

1197 
val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) 
18658  1198 
(map (fn (((i, _), T), tname) => 
1199 
HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $ 

22311  1200 
fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1)) 
1201 
(Free (tname, T)))) 

18658  1202 
(descr'' ~~ recTs ~~ tnames))); 
1203 

28731  1204 
val fin_set_supp = map (fn s => 
1205 
at_inst_of thy9 s RS at_fin_set_supp) dt_atoms; 

1206 
val fin_set_fresh = map (fn s => 

1207 
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

1208 
val pt1_atoms = map (fn Type (s, _) => 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1209 
Global_Theory.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

1210 
val pt2_atoms = map (fn Type (s, _) => 
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1211 
Global_Theory.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1212 
val exists_fresh' = Global_Theory.get_thms thy9 "exists_fresh'"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1213 
val fs_atoms = Global_Theory.get_thms thy9 "fin_supp"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1214 
val abs_supp = Global_Theory.get_thms thy9 "abs_supp"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1215 
val perm_fresh_fresh = Global_Theory.get_thms thy9 "perm_fresh_fresh"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1216 
val calc_atm = Global_Theory.get_thms thy9 "calc_atm"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1217 
val fresh_atm = Global_Theory.get_thms thy9 "fresh_atm"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1218 
val fresh_left = Global_Theory.get_thms thy9 "fresh_left"; 
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is globalonly;
wenzelm
parents:
39159
diff
changeset

1219 
val perm_swap = Global_Theory.get_thms thy9 "perm_swap"; 
18658  1220 

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

1221 
fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) = 
18658  1222 
let 
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1223 
val p = foldr1 HOLogic.mk_prod (ts @ freshs1); 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1224 
val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset

1225 
(HOLogic.exists_const T $ Abs ("x", T, 
6ebe26bfed18
Reimplemented proof of strong induction theorem.
ber 