wenzelm@404
|
1 |
(* Title: Pure/axclass.ML
|
wenzelm@404
|
2 |
Author: Markus Wenzel, TU Muenchen
|
wenzelm@404
|
3 |
|
wenzelm@24964
|
4 |
Type classes defined as predicates, associated with a record of
|
wenzelm@24964
|
5 |
parameters.
|
wenzelm@404
|
6 |
*)
|
wenzelm@404
|
7 |
|
wenzelm@404
|
8 |
signature AX_CLASS =
|
wenzelm@3938
|
9 |
sig
|
wenzelm@30344
|
10 |
val define_class: binding * class list -> string list ->
|
wenzelm@30211
|
11 |
(Thm.binding * term list) list -> theory -> class * theory
|
haftmann@24589
|
12 |
val add_classrel: thm -> theory -> theory
|
haftmann@24589
|
13 |
val add_arity: thm -> theory -> theory
|
haftmann@24589
|
14 |
val prove_classrel: class * class -> tactic -> theory -> theory
|
haftmann@24589
|
15 |
val prove_arity: string * sort list * sort -> tactic -> theory -> theory
|
wenzelm@36327
|
16 |
type info = {def: thm, intro: thm, axioms: thm list, params: (string * typ) list}
|
wenzelm@36327
|
17 |
val get_info: theory -> class -> info
|
wenzelm@19243
|
18 |
val class_intros: theory -> thm list
|
haftmann@20107
|
19 |
val class_of_param: theory -> string -> class option
|
wenzelm@19405
|
20 |
val cert_classrel: theory -> class * class -> class * class
|
wenzelm@19405
|
21 |
val read_classrel: theory -> xstring * xstring -> class * class
|
wenzelm@30344
|
22 |
val axiomatize_class: binding * class list -> theory -> theory
|
wenzelm@30344
|
23 |
val axiomatize_class_cmd: binding * xstring list -> theory -> theory
|
wenzelm@24929
|
24 |
val axiomatize_classrel: (class * class) list -> theory -> theory
|
wenzelm@24929
|
25 |
val axiomatize_classrel_cmd: (xstring * xstring) list -> theory -> theory
|
wenzelm@24929
|
26 |
val axiomatize_arity: arity -> theory -> theory
|
wenzelm@24929
|
27 |
val axiomatize_arity_cmd: xstring * string list * string -> theory -> theory
|
haftmann@25486
|
28 |
val instance_name: string * class -> string
|
haftmann@25597
|
29 |
val declare_overloaded: string * typ -> theory -> term * theory
|
haftmann@30519
|
30 |
val define_overloaded: binding -> string * term -> theory -> thm * theory
|
haftmann@25597
|
31 |
val unoverload: theory -> thm -> thm
|
haftmann@25597
|
32 |
val overload: theory -> thm -> thm
|
haftmann@25597
|
33 |
val unoverload_conv: theory -> conv
|
haftmann@25597
|
34 |
val overload_conv: theory -> conv
|
haftmann@25597
|
35 |
val unoverload_const: theory -> string * typ -> string
|
haftmann@31249
|
36 |
val lookup_inst_param: Consts.T -> ((string * string) * 'a) list -> string * typ -> 'a option
|
haftmann@25597
|
37 |
val param_of_inst: theory -> string * string -> string
|
haftmann@25597
|
38 |
val inst_of_param: theory -> string -> (string * string) option
|
wenzelm@33172
|
39 |
val thynames_of_arity: theory -> class * string -> string list
|
wenzelm@3938
|
40 |
end;
|
wenzelm@404
|
41 |
|
wenzelm@15801
|
42 |
structure AxClass: AX_CLASS =
|
wenzelm@404
|
43 |
struct
|
wenzelm@404
|
44 |
|
wenzelm@19405
|
45 |
(** theory data **)
|
wenzelm@423
|
46 |
|
wenzelm@19405
|
47 |
(* class parameters (canonical order) *)
|
wenzelm@423
|
48 |
|
wenzelm@19405
|
49 |
type param = string * class;
|
wenzelm@423
|
50 |
|
wenzelm@19405
|
51 |
fun add_param pp ((x, c): param) params =
|
wenzelm@19405
|
52 |
(case AList.lookup (op =) params x of
|
wenzelm@19405
|
53 |
NONE => (x, c) :: params
|
wenzelm@19405
|
54 |
| SOME c' => error ("Duplicate class parameter " ^ quote x ^
|
wenzelm@19405
|
55 |
" for " ^ Pretty.string_of_sort pp [c] ^
|
wenzelm@19405
|
56 |
(if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
|
wenzelm@423
|
57 |
|
wenzelm@19405
|
58 |
fun merge_params _ ([], qs) = qs
|
wenzelm@19405
|
59 |
| merge_params pp (ps, qs) =
|
wenzelm@19405
|
60 |
fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
|
wenzelm@423
|
61 |
|
wenzelm@423
|
62 |
|
wenzelm@36327
|
63 |
(* axclass info *)
|
wenzelm@6379
|
64 |
|
wenzelm@36327
|
65 |
type info =
|
wenzelm@19460
|
66 |
{def: thm,
|
wenzelm@19392
|
67 |
intro: thm,
|
haftmann@21463
|
68 |
axioms: thm list,
|
haftmann@21925
|
69 |
params: (string * typ) list};
|
wenzelm@19392
|
70 |
|
wenzelm@36327
|
71 |
type axclasses = info Symtab.table * param list;
|
wenzelm@19392
|
72 |
|
wenzelm@36327
|
73 |
fun make_axclass ((def, intro, axioms), params): info =
|
haftmann@27397
|
74 |
{def = def, intro = intro, axioms = axioms, params = params};
|
wenzelm@19405
|
75 |
|
wenzelm@19405
|
76 |
fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
|
wenzelm@19405
|
77 |
(Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
|
wenzelm@19405
|
78 |
|
wenzelm@19392
|
79 |
|
wenzelm@19392
|
80 |
(* instances *)
|
wenzelm@19392
|
81 |
|
wenzelm@20628
|
82 |
val classrel_prefix = "classrel_";
|
wenzelm@20628
|
83 |
val arity_prefix = "arity_";
|
wenzelm@19511
|
84 |
|
wenzelm@19574
|
85 |
type instances =
|
wenzelm@36325
|
86 |
(thm * proof) Symreltab.table * (*classrel theorems*)
|
wenzelm@36325
|
87 |
((class * sort list) * ((thm * string) * proof)) list Symtab.table; (*arity theorems with theory name*)
|
wenzelm@6379
|
88 |
|
wenzelm@36325
|
89 |
(*transitive closure of classrels and arity completion is done in Theory.at_begin hook*)
|
wenzelm@19574
|
90 |
fun merge_instances ((classrel1, arities1): instances, (classrel2, arities2)) =
|
wenzelm@36325
|
91 |
(Symreltab.join (K fst) (classrel1, classrel2),
|
wenzelm@19574
|
92 |
Symtab.join (K (merge (eq_fst op =))) (arities1, arities2));
|
wenzelm@19392
|
93 |
|
wenzelm@19392
|
94 |
|
haftmann@25597
|
95 |
(* instance parameters *)
|
haftmann@25597
|
96 |
|
haftmann@25597
|
97 |
type inst_params =
|
haftmann@25597
|
98 |
(string * thm) Symtab.table Symtab.table
|
haftmann@25597
|
99 |
(*constant name ~> type constructor ~> (constant name, equation)*)
|
haftmann@25597
|
100 |
* (string * string) Symtab.table; (*constant name ~> (constant name, type constructor)*)
|
haftmann@25597
|
101 |
|
haftmann@25597
|
102 |
fun merge_inst_params ((const_param1, param_const1), (const_param2, param_const2)) =
|
haftmann@25597
|
103 |
(Symtab.join (K (Symtab.merge (K true))) (const_param1, const_param2),
|
haftmann@25597
|
104 |
Symtab.merge (K true) (param_const1, param_const2));
|
haftmann@25597
|
105 |
|
haftmann@25597
|
106 |
|
wenzelm@19511
|
107 |
(* setup data *)
|
wenzelm@19392
|
108 |
|
wenzelm@36327
|
109 |
structure Data = Theory_Data_PP
|
wenzelm@22846
|
110 |
(
|
wenzelm@36325
|
111 |
type T = axclasses * ((instances * inst_params) * (class * class) list);
|
wenzelm@36325
|
112 |
val empty = ((Symtab.empty, []), (((Symreltab.empty, Symtab.empty), (Symtab.empty, Symtab.empty)), []));
|
wenzelm@19574
|
113 |
val extend = I;
|
wenzelm@36325
|
114 |
fun merge pp ((axclasses1, ((instances1, inst_params1), diff_merge_classrels1)),
|
wenzelm@36325
|
115 |
(axclasses2, ((instances2, inst_params2), diff_merge_classrels2))) =
|
wenzelm@36325
|
116 |
let
|
wenzelm@36327
|
117 |
val (classrels1, classrels2) = pairself (Symreltab.keys o fst) (instances1, instances2);
|
wenzelm@36327
|
118 |
val diff_merge_classrels =
|
wenzelm@36327
|
119 |
subtract (op =) classrels1 classrels2 @
|
wenzelm@36327
|
120 |
subtract (op =) classrels2 classrels1 @
|
wenzelm@36327
|
121 |
diff_merge_classrels1 @ diff_merge_classrels2;
|
wenzelm@36325
|
122 |
in
|
wenzelm@36325
|
123 |
(merge_axclasses pp (axclasses1, axclasses2),
|
wenzelm@36325
|
124 |
((merge_instances (instances1, instances2), merge_inst_params (inst_params1, inst_params2)),
|
wenzelm@36325
|
125 |
diff_merge_classrels))
|
wenzelm@36325
|
126 |
end;
|
wenzelm@22846
|
127 |
);
|
wenzelm@6379
|
128 |
|
wenzelm@6379
|
129 |
|
wenzelm@19574
|
130 |
(* maintain axclasses *)
|
wenzelm@19392
|
131 |
|
wenzelm@36327
|
132 |
val get_axclasses = #1 o Data.get;
|
wenzelm@36327
|
133 |
val map_axclasses = Data.map o apfst;
|
wenzelm@6379
|
134 |
|
wenzelm@24929
|
135 |
fun get_info thy c =
|
wenzelm@36327
|
136 |
(case Symtab.lookup (#1 (get_axclasses thy)) c of
|
wenzelm@36327
|
137 |
SOME info => info
|
wenzelm@21919
|
138 |
| NONE => error ("No such axclass: " ^ quote c));
|
wenzelm@6379
|
139 |
|
wenzelm@19123
|
140 |
fun class_intros thy =
|
wenzelm@19392
|
141 |
let
|
wenzelm@36327
|
142 |
fun add_intro c = (case try (get_info thy) c of SOME {intro, ...} => cons intro | _ => I);
|
wenzelm@21931
|
143 |
val classes = Sign.all_classes thy;
|
wenzelm@19392
|
144 |
in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
|
wenzelm@15876
|
145 |
|
wenzelm@36327
|
146 |
fun all_params_of thy S =
|
wenzelm@19574
|
147 |
let val params = #2 (get_axclasses thy);
|
wenzelm@36327
|
148 |
in fold (fn (x, c) => if Sign.subsort thy (S, [c]) then cons x else I) params [] end;
|
wenzelm@19460
|
149 |
|
wenzelm@24964
|
150 |
fun class_of_param thy = AList.lookup (op =) (#2 (get_axclasses thy));
|
wenzelm@19460
|
151 |
|
wenzelm@21919
|
152 |
|
wenzelm@19511
|
153 |
(* maintain instances *)
|
wenzelm@19503
|
154 |
|
wenzelm@30364
|
155 |
fun instance_name (a, c) = Long_Name.base_name c ^ "_" ^ Long_Name.base_name a;
|
haftmann@25486
|
156 |
|
wenzelm@36327
|
157 |
val get_instances = #1 o #1 o #2 o Data.get;
|
wenzelm@36327
|
158 |
val map_instances = Data.map o apsnd o apfst o apfst;
|
wenzelm@36325
|
159 |
|
wenzelm@36327
|
160 |
val get_diff_merge_classrels = #2 o #2 o Data.get;
|
wenzelm@36327
|
161 |
val clear_diff_merge_classrels = Data.map (apsnd (apsnd (K [])));
|
wenzelm@19528
|
162 |
|
wenzelm@19528
|
163 |
|
wenzelm@19574
|
164 |
fun the_classrel thy (c1, c2) =
|
wenzelm@36325
|
165 |
(case Symreltab.lookup (#1 (get_instances thy)) (c1, c2) of
|
wenzelm@36325
|
166 |
SOME classrel => classrel
|
wenzelm@24920
|
167 |
| NONE => error ("Unproven class relation " ^
|
wenzelm@24920
|
168 |
Syntax.string_of_classrel (ProofContext.init thy) [c1, c2]));
|
wenzelm@19574
|
169 |
|
wenzelm@36325
|
170 |
fun the_classrel_thm thy = Thm.transfer thy o fst o the_classrel thy;
|
wenzelm@36325
|
171 |
fun the_classrel_prf thy = snd o the_classrel thy;
|
wenzelm@36325
|
172 |
|
wenzelm@36325
|
173 |
fun put_trancl_classrel ((c1, c2), th) thy =
|
wenzelm@36325
|
174 |
let
|
wenzelm@36327
|
175 |
val cert = Thm.cterm_of thy;
|
wenzelm@36327
|
176 |
val certT = Thm.ctyp_of thy;
|
wenzelm@36327
|
177 |
|
wenzelm@36327
|
178 |
val classrels = fst (get_instances thy);
|
wenzelm@36328
|
179 |
val classes = Sorts.classes_of (Sign.classes_of thy);
|
wenzelm@36325
|
180 |
|
wenzelm@36325
|
181 |
fun reflcl_classrel (c1', c2') =
|
wenzelm@36327
|
182 |
if c1' = c2'
|
wenzelm@36327
|
183 |
then Thm.trivial (cert (Logic.mk_of_class (TVar ((Name.aT, 0), []), c1')))
|
wenzelm@36327
|
184 |
else the_classrel_thm thy (c1', c2');
|
wenzelm@36325
|
185 |
fun gen_classrel (c1_pred, c2_succ) =
|
wenzelm@36325
|
186 |
let
|
wenzelm@36325
|
187 |
val th' = ((reflcl_classrel (c1_pred, c1) RS th) RS reflcl_classrel (c2, c2_succ))
|
wenzelm@36327
|
188 |
|> Drule.instantiate' [SOME (certT (TVar ((Name.aT, 0), [])))] []
|
wenzelm@36327
|
189 |
|> Thm.close_derivation;
|
wenzelm@36327
|
190 |
val prf' = th' |> Thm.proof_of;
|
wenzelm@36327
|
191 |
in ((c1_pred, c2_succ), (th', prf')) end;
|
wenzelm@36325
|
192 |
|
wenzelm@36327
|
193 |
val new_classrels =
|
wenzelm@36327
|
194 |
Library.map_product pair (c1 :: Graph.imm_preds classes c1) (c2 :: Graph.imm_succs classes c2)
|
wenzelm@36325
|
195 |
|> filter_out (Symreltab.defined classrels)
|
wenzelm@36327
|
196 |
|> map gen_classrel;
|
wenzelm@36327
|
197 |
val needed = not (null new_classrels);
|
wenzelm@36325
|
198 |
in
|
wenzelm@36325
|
199 |
(needed,
|
wenzelm@36325
|
200 |
if needed then
|
wenzelm@36325
|
201 |
thy |> map_instances (fn (classrels, arities) =>
|
wenzelm@36325
|
202 |
(classrels |> fold Symreltab.update new_classrels, arities))
|
wenzelm@36325
|
203 |
else thy)
|
wenzelm@36325
|
204 |
end;
|
wenzelm@36325
|
205 |
|
wenzelm@36325
|
206 |
fun complete_classrels thy =
|
wenzelm@36325
|
207 |
let
|
wenzelm@36327
|
208 |
val diff_merge_classrels = get_diff_merge_classrels thy;
|
wenzelm@36327
|
209 |
val classrels = fst (get_instances thy);
|
wenzelm@36325
|
210 |
val (needed, thy') = (false, thy) |>
|
wenzelm@36325
|
211 |
fold (fn c12 => fn (needed, thy) =>
|
wenzelm@36325
|
212 |
put_trancl_classrel (c12, Symreltab.lookup classrels c12 |> the |> fst) thy
|
wenzelm@36325
|
213 |
|>> (fn b => needed orelse b))
|
wenzelm@36327
|
214 |
diff_merge_classrels;
|
wenzelm@36325
|
215 |
in
|
wenzelm@36325
|
216 |
if null diff_merge_classrels then NONE
|
wenzelm@36325
|
217 |
else thy' |> clear_diff_merge_classrels |> SOME
|
wenzelm@36325
|
218 |
end;
|
wenzelm@19503
|
219 |
|
wenzelm@19503
|
220 |
|
wenzelm@19574
|
221 |
fun the_arity thy a (c, Ss) =
|
wenzelm@24929
|
222 |
(case AList.lookup (op =) (Symtab.lookup_list (#2 (get_instances thy)) a) (c, Ss) of
|
wenzelm@36325
|
223 |
SOME arity => arity
|
wenzelm@24920
|
224 |
| NONE => error ("Unproven type arity " ^
|
wenzelm@24920
|
225 |
Syntax.string_of_arity (ProofContext.init thy) (a, Ss, [c])));
|
wenzelm@19503
|
226 |
|
wenzelm@36325
|
227 |
fun the_arity_thm thy a c_Ss = the_arity thy a c_Ss |> fst |> fst |> Thm.transfer thy;
|
wenzelm@36325
|
228 |
fun the_arity_prf thy a c_Ss = the_arity thy a c_Ss |> snd;
|
wenzelm@36325
|
229 |
|
wenzelm@33172
|
230 |
fun thynames_of_arity thy (c, a) =
|
wenzelm@33172
|
231 |
Symtab.lookup_list (#2 (get_instances thy)) a
|
wenzelm@36325
|
232 |
|> map_filter (fn ((c', _), ((_, name),_)) => if c = c' then SOME name else NONE)
|
haftmann@27497
|
233 |
|> rev;
|
haftmann@27397
|
234 |
|
wenzelm@36325
|
235 |
fun insert_arity_completions thy (t, ((c, Ss), ((th, thy_name), _))) arities =
|
haftmann@27547
|
236 |
let
|
haftmann@27547
|
237 |
val algebra = Sign.classes_of thy;
|
wenzelm@33172
|
238 |
val super_class_completions =
|
wenzelm@33172
|
239 |
Sign.super_classes thy c
|
haftmann@27547
|
240 |
|> filter_out (fn c1 => exists (fn ((c2, Ss2), _) => c1 = c2
|
wenzelm@33172
|
241 |
andalso Sorts.sorts_le algebra (Ss2, Ss)) (Symtab.lookup_list arities t));
|
wenzelm@36325
|
242 |
val names_and_Ss = Name.names Name.context Name.aT (map (K []) Ss);
|
wenzelm@36325
|
243 |
val completions = super_class_completions |> map (fn c1 =>
|
wenzelm@36325
|
244 |
let
|
wenzelm@36325
|
245 |
val th1 = (th RS the_classrel_thm thy (c, c1))
|
wenzelm@36325
|
246 |
|> Drule.instantiate' (map (SOME o ctyp_of thy o TVar o apfst (rpair 0)) names_and_Ss) []
|
wenzelm@36327
|
247 |
|> Thm.close_derivation;
|
wenzelm@36327
|
248 |
val prf1 = Thm.proof_of th1;
|
wenzelm@36327
|
249 |
in (((th1, thy_name), prf1), c1) end);
|
wenzelm@36325
|
250 |
val arities' = fold (fn (th_thy_prf1, c1) => Symtab.cons_list (t, ((c1, Ss), th_thy_prf1)))
|
haftmann@27547
|
251 |
completions arities;
|
wenzelm@33172
|
252 |
in (null completions, arities') end;
|
wenzelm@19503
|
253 |
|
haftmann@27547
|
254 |
fun put_arity ((t, Ss, c), th) thy =
|
haftmann@27547
|
255 |
let
|
wenzelm@36325
|
256 |
val arity' = (t, ((c, Ss), ((th, Context.theory_name thy), Thm.proof_of th)));
|
haftmann@27547
|
257 |
in
|
haftmann@27547
|
258 |
thy
|
haftmann@27547
|
259 |
|> map_instances (fn (classrel, arities) => (classrel,
|
haftmann@27547
|
260 |
arities
|
haftmann@27547
|
261 |
|> Symtab.insert_list (eq_fst op =) arity'
|
haftmann@27547
|
262 |
|> insert_arity_completions thy arity'
|
haftmann@27547
|
263 |
|> snd))
|
haftmann@27547
|
264 |
end;
|
wenzelm@19503
|
265 |
|
wenzelm@31944
|
266 |
fun complete_arities thy =
|
haftmann@27547
|
267 |
let
|
haftmann@27547
|
268 |
val arities = snd (get_instances thy);
|
wenzelm@33172
|
269 |
val (finished, arities') = arities
|
wenzelm@33172
|
270 |
|> fold_map (insert_arity_completions thy) (Symtab.dest_list arities);
|
wenzelm@33172
|
271 |
in
|
wenzelm@33172
|
272 |
if forall I finished then NONE
|
haftmann@27547
|
273 |
else SOME (thy |> map_instances (fn (classrel, _) => (classrel, arities')))
|
haftmann@27547
|
274 |
end;
|
haftmann@27547
|
275 |
|
wenzelm@36325
|
276 |
val _ = Context.>> (Context.map_theory
|
wenzelm@36325
|
277 |
(Theory.at_begin complete_classrels #> Theory.at_begin complete_arities))
|
haftmann@27397
|
278 |
|
haftmann@27397
|
279 |
|
haftmann@25597
|
280 |
(* maintain instance parameters *)
|
haftmann@25597
|
281 |
|
wenzelm@36327
|
282 |
val get_inst_params = #2 o #1 o #2 o Data.get;
|
wenzelm@36327
|
283 |
val map_inst_params = Data.map o apsnd o apfst o apsnd;
|
haftmann@25597
|
284 |
|
haftmann@25597
|
285 |
fun get_inst_param thy (c, tyco) =
|
wenzelm@36327
|
286 |
(case Symtab.lookup (the_default Symtab.empty (Symtab.lookup (#1 (get_inst_params thy)) c)) tyco of
|
wenzelm@36327
|
287 |
SOME c' => c'
|
wenzelm@36327
|
288 |
| NONE => error ("No instance parameter for constant " ^ quote c ^ " on type " ^ quote tyco));
|
haftmann@25597
|
289 |
|
wenzelm@36327
|
290 |
fun add_inst_param (c, tyco) inst =
|
wenzelm@36327
|
291 |
(map_inst_params o apfst o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
|
haftmann@25597
|
292 |
#> (map_inst_params o apsnd) (Symtab.update_new (fst inst, (c, tyco)));
|
haftmann@25597
|
293 |
|
haftmann@25597
|
294 |
val inst_of_param = Symtab.lookup o snd o get_inst_params;
|
haftmann@25597
|
295 |
val param_of_inst = fst oo get_inst_param;
|
haftmann@25597
|
296 |
|
wenzelm@36327
|
297 |
fun inst_thms thy =
|
wenzelm@36327
|
298 |
(Symtab.fold (Symtab.fold (cons o snd o snd) o snd) o fst) (get_inst_params thy) [];
|
haftmann@25597
|
299 |
|
haftmann@31249
|
300 |
fun get_inst_tyco consts = try (fst o dest_Type o the_single o Consts.typargs consts);
|
haftmann@25597
|
301 |
|
haftmann@25597
|
302 |
fun unoverload thy = MetaSimplifier.simplify true (inst_thms thy);
|
haftmann@25597
|
303 |
fun overload thy = MetaSimplifier.simplify true (map Thm.symmetric (inst_thms thy));
|
haftmann@25597
|
304 |
|
haftmann@25597
|
305 |
fun unoverload_conv thy = MetaSimplifier.rewrite true (inst_thms thy);
|
haftmann@25597
|
306 |
fun overload_conv thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));
|
haftmann@25597
|
307 |
|
wenzelm@36327
|
308 |
fun lookup_inst_param consts params (c, T) =
|
wenzelm@36327
|
309 |
(case get_inst_tyco consts (c, T) of
|
wenzelm@36327
|
310 |
SOME tyco => AList.lookup (op =) params (c, tyco)
|
wenzelm@36327
|
311 |
| NONE => NONE);
|
haftmann@31249
|
312 |
|
haftmann@25597
|
313 |
fun unoverload_const thy (c_ty as (c, _)) =
|
wenzelm@36327
|
314 |
if is_some (class_of_param thy c) then
|
wenzelm@36327
|
315 |
(case get_inst_tyco (Sign.consts_of thy) c_ty of
|
wenzelm@36327
|
316 |
SOME tyco => try (param_of_inst thy) (c, tyco) |> the_default c
|
wenzelm@36327
|
317 |
| NONE => c)
|
haftmann@33969
|
318 |
else c;
|
haftmann@25597
|
319 |
|
wenzelm@404
|
320 |
|
wenzelm@36327
|
321 |
|
wenzelm@19511
|
322 |
(** instances **)
|
wenzelm@19418
|
323 |
|
wenzelm@19418
|
324 |
(* class relations *)
|
wenzelm@19418
|
325 |
|
wenzelm@19405
|
326 |
fun cert_classrel thy raw_rel =
|
wenzelm@15876
|
327 |
let
|
wenzelm@26939
|
328 |
val string_of_sort = Syntax.string_of_sort_global thy;
|
wenzelm@19405
|
329 |
val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
|
wenzelm@24271
|
330 |
val _ = Sign.primitive_classrel (c1, c2) (Theory.copy thy);
|
wenzelm@19405
|
331 |
val _ =
|
wenzelm@19460
|
332 |
(case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of
|
wenzelm@19405
|
333 |
[] => ()
|
wenzelm@26939
|
334 |
| xs => raise TYPE ("Class " ^ string_of_sort [c1] ^ " lacks parameter(s) " ^
|
wenzelm@26939
|
335 |
commas_quote xs ^ " of " ^ string_of_sort [c2], [], []));
|
wenzelm@19405
|
336 |
in (c1, c2) end;
|
wenzelm@19405
|
337 |
|
wenzelm@19405
|
338 |
fun read_classrel thy raw_rel =
|
wenzelm@35669
|
339 |
cert_classrel thy (pairself (ProofContext.read_class (ProofContext.init thy)) raw_rel)
|
wenzelm@19405
|
340 |
handle TYPE (msg, _, _) => error msg;
|
wenzelm@19405
|
341 |
|
wenzelm@36327
|
342 |
val shyps_topped = forall null o #shyps o Thm.rep_thm;
|
wenzelm@36327
|
343 |
|
wenzelm@19405
|
344 |
|
haftmann@25597
|
345 |
(* declaration and definition of instances of overloaded constants *)
|
haftmann@25597
|
346 |
|
wenzelm@35201
|
347 |
fun inst_tyco_of thy (c, T) =
|
wenzelm@35201
|
348 |
(case get_inst_tyco (Sign.consts_of thy) (c, T) of
|
wenzelm@35201
|
349 |
SOME tyco => tyco
|
wenzelm@35201
|
350 |
| NONE => error ("Illegal type for instantiation of class parameter: " ^
|
wenzelm@35201
|
351 |
quote (c ^ " :: " ^ Syntax.string_of_typ_global thy T)));
|
haftmann@31249
|
352 |
|
haftmann@25597
|
353 |
fun declare_overloaded (c, T) thy =
|
haftmann@25597
|
354 |
let
|
wenzelm@35201
|
355 |
val class =
|
wenzelm@35201
|
356 |
(case class_of_param thy c of
|
wenzelm@35201
|
357 |
SOME class => class
|
wenzelm@35201
|
358 |
| NONE => error ("Not a class parameter: " ^ quote c));
|
haftmann@31249
|
359 |
val tyco = inst_tyco_of thy (c, T);
|
haftmann@25597
|
360 |
val name_inst = instance_name (tyco, class) ^ "_inst";
|
wenzelm@30364
|
361 |
val c' = Long_Name.base_name c ^ "_" ^ Long_Name.base_name tyco;
|
haftmann@25597
|
362 |
val T' = Type.strip_sorts T;
|
haftmann@25597
|
363 |
in
|
haftmann@25597
|
364 |
thy
|
wenzelm@35201
|
365 |
|> Sign.qualified_path true (Binding.name name_inst)
|
wenzelm@33173
|
366 |
|> Sign.declare_const ((Binding.name c', T'), NoSyn)
|
wenzelm@30344
|
367 |
|-> (fn const' as Const (c'', _) =>
|
wenzelm@30344
|
368 |
Thm.add_def false true
|
wenzelm@30344
|
369 |
(Binding.name (Thm.def_name c'), Logic.mk_equals (Const (c, T'), const'))
|
wenzelm@36106
|
370 |
#>> apsnd Thm.varifyT_global
|
wenzelm@36106
|
371 |
#-> (fn (_, thm) => add_inst_param (c, tyco) (c'', thm)
|
wenzelm@36106
|
372 |
#> PureThy.add_thm ((Binding.conceal (Binding.name c'), thm), [])
|
wenzelm@36106
|
373 |
#> snd
|
wenzelm@36106
|
374 |
#> pair (Const (c, T))))
|
wenzelm@35201
|
375 |
||> Sign.restore_naming thy
|
haftmann@25597
|
376 |
end;
|
haftmann@25597
|
377 |
|
haftmann@30519
|
378 |
fun define_overloaded b (c, t) thy =
|
haftmann@25597
|
379 |
let
|
haftmann@25597
|
380 |
val T = Term.fastype_of t;
|
haftmann@31249
|
381 |
val tyco = inst_tyco_of thy (c, T);
|
haftmann@25597
|
382 |
val (c', eq) = get_inst_param thy (c, tyco);
|
haftmann@25597
|
383 |
val prop = Logic.mk_equals (Const (c', T), t);
|
haftmann@30519
|
384 |
val b' = Thm.def_binding_optional
|
haftmann@30519
|
385 |
(Binding.name (Long_Name.base_name c ^ "_" ^ Long_Name.base_name tyco)) b;
|
haftmann@25597
|
386 |
in
|
haftmann@25597
|
387 |
thy
|
haftmann@30519
|
388 |
|> Thm.add_def false false (b', prop)
|
wenzelm@36106
|
389 |
|>> (fn (_, thm) => Drule.transitive_thm OF [eq, thm])
|
haftmann@25597
|
390 |
end;
|
haftmann@25597
|
391 |
|
haftmann@25597
|
392 |
|
haftmann@30951
|
393 |
(* primitive rules *)
|
haftmann@30951
|
394 |
|
wenzelm@31948
|
395 |
fun add_classrel raw_th thy =
|
haftmann@30951
|
396 |
let
|
wenzelm@31948
|
397 |
val th = Thm.strip_shyps (Thm.transfer thy raw_th);
|
wenzelm@31948
|
398 |
val prop = Thm.plain_prop_of th;
|
haftmann@30951
|
399 |
fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
|
haftmann@30951
|
400 |
val rel = Logic.dest_classrel prop handle TERM _ => err ();
|
haftmann@30951
|
401 |
val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
|
wenzelm@36325
|
402 |
val th' = th
|
wenzelm@36325
|
403 |
|> Drule.instantiate' [SOME (ctyp_of thy (TVar ((Name.aT, 0), [c1])))] []
|
wenzelm@36325
|
404 |
|> Drule.unconstrainTs;
|
wenzelm@36327
|
405 |
val _ = shyps_topped th' orelse raise Fail "add_classrel: nontop shyps after unconstrain";
|
haftmann@30951
|
406 |
in
|
haftmann@30951
|
407 |
thy
|
haftmann@30951
|
408 |
|> Sign.primitive_classrel (c1, c2)
|
wenzelm@36325
|
409 |
|> (snd oo put_trancl_classrel) ((c1, c2), th')
|
haftmann@30951
|
410 |
|> perhaps complete_arities
|
haftmann@30951
|
411 |
end;
|
haftmann@30951
|
412 |
|
wenzelm@31948
|
413 |
fun add_arity raw_th thy =
|
haftmann@30951
|
414 |
let
|
wenzelm@31948
|
415 |
val th = Thm.strip_shyps (Thm.transfer thy raw_th);
|
wenzelm@31948
|
416 |
val prop = Thm.plain_prop_of th;
|
haftmann@30951
|
417 |
fun err () = raise THM ("add_arity: malformed type arity", 0, [th]);
|
haftmann@30951
|
418 |
val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err ();
|
wenzelm@36325
|
419 |
val names = Name.names Name.context Name.aT Ss;
|
wenzelm@36325
|
420 |
val T = Type (t, map TFree names);
|
haftmann@30951
|
421 |
val missing_params = Sign.complete_sort thy [c]
|
haftmann@30951
|
422 |
|> maps (these o Option.map #params o try (get_info thy))
|
haftmann@30951
|
423 |
|> filter_out (fn (const, _) => can (get_inst_param thy) (const, t))
|
haftmann@30951
|
424 |
|> (map o apsnd o map_atyps) (K T);
|
haftmann@30951
|
425 |
val _ = map (Sign.certify_sort thy) Ss = Ss orelse err ();
|
wenzelm@36325
|
426 |
val th' = th
|
wenzelm@36325
|
427 |
|> Drule.instantiate' (map (SOME o ctyp_of thy o TVar o apfst (rpair 0)) names) []
|
wenzelm@36325
|
428 |
|> Drule.unconstrainTs;
|
wenzelm@36327
|
429 |
val _ = shyps_topped th' orelse raise Fail "add_arity: nontop shyps after unconstrain";
|
haftmann@30951
|
430 |
in
|
haftmann@30951
|
431 |
thy
|
haftmann@30951
|
432 |
|> fold (snd oo declare_overloaded) missing_params
|
haftmann@30951
|
433 |
|> Sign.primitive_arity (t, Ss, [c])
|
wenzelm@36325
|
434 |
|> put_arity ((t, Ss, c), th')
|
haftmann@30951
|
435 |
end;
|
haftmann@30951
|
436 |
|
haftmann@30951
|
437 |
|
haftmann@30951
|
438 |
(* tactical proofs *)
|
haftmann@30951
|
439 |
|
haftmann@30951
|
440 |
fun prove_classrel raw_rel tac thy =
|
haftmann@30951
|
441 |
let
|
haftmann@30951
|
442 |
val ctxt = ProofContext.init thy;
|
haftmann@30951
|
443 |
val (c1, c2) = cert_classrel thy raw_rel;
|
haftmann@30951
|
444 |
val th = Goal.prove ctxt [] [] (Logic.mk_classrel (c1, c2)) (K tac) handle ERROR msg =>
|
haftmann@30951
|
445 |
cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
|
haftmann@30951
|
446 |
quote (Syntax.string_of_classrel ctxt [c1, c2]));
|
haftmann@30951
|
447 |
in
|
haftmann@30951
|
448 |
thy
|
haftmann@30951
|
449 |
|> PureThy.add_thms [((Binding.name
|
haftmann@30951
|
450 |
(prefix classrel_prefix (Logic.name_classrel (c1, c2))), th), [])]
|
haftmann@30951
|
451 |
|-> (fn [th'] => add_classrel th')
|
haftmann@30951
|
452 |
end;
|
haftmann@30951
|
453 |
|
haftmann@30951
|
454 |
fun prove_arity raw_arity tac thy =
|
haftmann@30951
|
455 |
let
|
haftmann@30951
|
456 |
val ctxt = ProofContext.init thy;
|
wenzelm@35669
|
457 |
val arity = ProofContext.cert_arity ctxt raw_arity;
|
haftmann@30951
|
458 |
val names = map (prefix arity_prefix) (Logic.name_arities arity);
|
haftmann@30951
|
459 |
val props = Logic.mk_arities arity;
|
haftmann@30951
|
460 |
val ths = Goal.prove_multi ctxt [] [] props
|
haftmann@30951
|
461 |
(fn _ => Goal.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
|
haftmann@30951
|
462 |
cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
|
haftmann@30951
|
463 |
quote (Syntax.string_of_arity ctxt arity));
|
haftmann@30951
|
464 |
in
|
haftmann@30951
|
465 |
thy
|
haftmann@30951
|
466 |
|> PureThy.add_thms (map (rpair []) (map Binding.name names ~~ ths))
|
haftmann@30951
|
467 |
|-> fold add_arity
|
haftmann@30951
|
468 |
end;
|
haftmann@30951
|
469 |
|
haftmann@30951
|
470 |
|
wenzelm@19511
|
471 |
|
wenzelm@19511
|
472 |
(** class definitions **)
|
wenzelm@19511
|
473 |
|
wenzelm@23421
|
474 |
fun split_defined n eq =
|
wenzelm@23421
|
475 |
let
|
wenzelm@23421
|
476 |
val intro =
|
wenzelm@23421
|
477 |
(eq RS Drule.equal_elim_rule2)
|
wenzelm@23421
|
478 |
|> Conjunction.curry_balanced n
|
wenzelm@23421
|
479 |
|> n = 0 ? Thm.eq_assumption 1;
|
wenzelm@23421
|
480 |
val dests =
|
wenzelm@23421
|
481 |
if n = 0 then []
|
wenzelm@23421
|
482 |
else
|
wenzelm@23421
|
483 |
(eq RS Drule.equal_elim_rule1)
|
wenzelm@32765
|
484 |
|> Balanced_Tree.dest (fn th =>
|
wenzelm@23421
|
485 |
(th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
|
wenzelm@23421
|
486 |
in (intro, dests) end;
|
wenzelm@23421
|
487 |
|
wenzelm@24964
|
488 |
fun define_class (bclass, raw_super) raw_params raw_specs thy =
|
wenzelm@19511
|
489 |
let
|
wenzelm@19511
|
490 |
val ctxt = ProofContext.init thy;
|
wenzelm@24964
|
491 |
val pp = Syntax.pp ctxt;
|
wenzelm@19511
|
492 |
|
wenzelm@19511
|
493 |
|
wenzelm@24964
|
494 |
(* class *)
|
wenzelm@19511
|
495 |
|
wenzelm@30344
|
496 |
val bconst = Binding.map_name Logic.const_of_class bclass;
|
wenzelm@30344
|
497 |
val class = Sign.full_name thy bclass;
|
wenzelm@24731
|
498 |
val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
|
wenzelm@19511
|
499 |
|
wenzelm@24964
|
500 |
fun check_constraint (a, S) =
|
wenzelm@24964
|
501 |
if Sign.subsort thy (super, S) then ()
|
wenzelm@24964
|
502 |
else error ("Sort constraint of type variable " ^
|
wenzelm@32966
|
503 |
setmp_CRITICAL show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
|
wenzelm@24964
|
504 |
" needs to be weaker than " ^ Pretty.string_of_sort pp super);
|
wenzelm@24964
|
505 |
|
wenzelm@24964
|
506 |
|
wenzelm@24964
|
507 |
(* params *)
|
wenzelm@24964
|
508 |
|
wenzelm@24964
|
509 |
val params = raw_params |> map (fn p =>
|
wenzelm@24964
|
510 |
let
|
wenzelm@24964
|
511 |
val T = Sign.the_const_type thy p;
|
wenzelm@24964
|
512 |
val _ =
|
wenzelm@24964
|
513 |
(case Term.add_tvarsT T [] of
|
wenzelm@24964
|
514 |
[((a, _), S)] => check_constraint (a, S)
|
wenzelm@24964
|
515 |
| _ => error ("Exactly one type variable expected in class parameter " ^ quote p));
|
wenzelm@24964
|
516 |
val T' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) T;
|
wenzelm@24964
|
517 |
in (p, T') end);
|
wenzelm@24964
|
518 |
|
wenzelm@24964
|
519 |
|
wenzelm@24964
|
520 |
(* axioms *)
|
wenzelm@24964
|
521 |
|
wenzelm@19511
|
522 |
fun prep_axiom t =
|
wenzelm@19511
|
523 |
(case Term.add_tfrees t [] of
|
wenzelm@24964
|
524 |
[(a, S)] => check_constraint (a, S)
|
wenzelm@24964
|
525 |
| [] => ()
|
wenzelm@24964
|
526 |
| _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t);
|
wenzelm@24964
|
527 |
t
|
wenzelm@24964
|
528 |
|> Term.map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
|
wenzelm@24964
|
529 |
|> Logic.close_form);
|
wenzelm@19511
|
530 |
|
wenzelm@24681
|
531 |
val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
|
haftmann@22745
|
532 |
val name_atts = map fst raw_specs;
|
wenzelm@19511
|
533 |
|
wenzelm@19511
|
534 |
|
wenzelm@19511
|
535 |
(* definition *)
|
wenzelm@19511
|
536 |
|
wenzelm@35854
|
537 |
val conjs = Logic.mk_of_sort (Term.aT [], super) @ flat axiomss;
|
wenzelm@19511
|
538 |
val class_eq =
|
wenzelm@31943
|
539 |
Logic.mk_equals (Logic.mk_of_class (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
|
wenzelm@19511
|
540 |
|
wenzelm@19511
|
541 |
val ([def], def_thy) =
|
wenzelm@19511
|
542 |
thy
|
wenzelm@19511
|
543 |
|> Sign.primitive_class (bclass, super)
|
wenzelm@35238
|
544 |
|> PureThy.add_defs false [((Thm.def_binding bconst, class_eq), [])];
|
wenzelm@19511
|
545 |
val (raw_intro, (raw_classrel, raw_axioms)) =
|
wenzelm@23421
|
546 |
split_defined (length conjs) def ||> chop (length super);
|
wenzelm@19392
|
547 |
|
wenzelm@19418
|
548 |
|
wenzelm@19511
|
549 |
(* facts *)
|
wenzelm@19511
|
550 |
|
wenzelm@19511
|
551 |
val class_triv = Thm.class_triv def_thy class;
|
wenzelm@19511
|
552 |
val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
|
wenzelm@19511
|
553 |
def_thy
|
wenzelm@35201
|
554 |
|> Sign.qualified_path true bconst
|
haftmann@27691
|
555 |
|> PureThy.note_thmss ""
|
wenzelm@36326
|
556 |
[((Binding.name "intro", []), [([Drule.export_without_context raw_intro], [])]),
|
wenzelm@36326
|
557 |
((Binding.name "super", []), [(map Drule.export_without_context raw_classrel, [])]),
|
wenzelm@36326
|
558 |
((Binding.name "axioms", []),
|
wenzelm@35021
|
559 |
[(map (fn th => Drule.export_without_context (class_triv RS th)) raw_axioms, [])])]
|
haftmann@27691
|
560 |
||> Sign.restore_naming def_thy;
|
wenzelm@19511
|
561 |
|
wenzelm@24847
|
562 |
|
wenzelm@19511
|
563 |
(* result *)
|
wenzelm@19511
|
564 |
|
wenzelm@24964
|
565 |
val axclass = make_axclass ((def, intro, axioms), params);
|
wenzelm@19511
|
566 |
val result_thy =
|
wenzelm@19511
|
567 |
facts_thy
|
wenzelm@36325
|
568 |
|> fold (snd oo put_trancl_classrel) (map (pair class) super ~~ classrel)
|
wenzelm@35201
|
569 |
|> Sign.qualified_path false bconst
|
haftmann@27691
|
570 |
|> PureThy.note_thmss "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
|
wenzelm@19511
|
571 |
|> Sign.restore_naming facts_thy
|
wenzelm@19574
|
572 |
|> map_axclasses (fn (axclasses, parameters) =>
|
wenzelm@21919
|
573 |
(Symtab.update (class, axclass) axclasses,
|
wenzelm@24964
|
574 |
fold (fn (x, _) => add_param pp (x, class)) params parameters));
|
wenzelm@19511
|
575 |
|
wenzelm@19511
|
576 |
in (class, result_thy) end;
|
wenzelm@19511
|
577 |
|
wenzelm@19511
|
578 |
|
wenzelm@19531
|
579 |
|
wenzelm@19511
|
580 |
(** axiomatizations **)
|
wenzelm@19511
|
581 |
|
wenzelm@19511
|
582 |
local
|
wenzelm@19511
|
583 |
|
wenzelm@35896
|
584 |
(* old-style axioms *)
|
wenzelm@35896
|
585 |
|
wenzelm@35896
|
586 |
fun add_axiom (b, prop) =
|
wenzelm@35896
|
587 |
Thm.add_axiom (b, prop) #->
|
wenzelm@36106
|
588 |
(fn (_, thm) => PureThy.add_thm ((b, Drule.export_without_context thm), []));
|
wenzelm@35896
|
589 |
|
wenzelm@20628
|
590 |
fun axiomatize prep mk name add raw_args thy =
|
wenzelm@20628
|
591 |
let
|
wenzelm@20628
|
592 |
val args = prep thy raw_args;
|
wenzelm@20628
|
593 |
val specs = mk args;
|
wenzelm@20628
|
594 |
val names = name args;
|
haftmann@29579
|
595 |
in
|
haftmann@29579
|
596 |
thy
|
wenzelm@35896
|
597 |
|> fold_map add_axiom (map Binding.name names ~~ specs)
|
haftmann@29579
|
598 |
|-> fold add
|
haftmann@29579
|
599 |
end;
|
wenzelm@19511
|
600 |
|
wenzelm@19511
|
601 |
fun ax_classrel prep =
|
wenzelm@20628
|
602 |
axiomatize (map o prep) (map Logic.mk_classrel)
|
wenzelm@20628
|
603 |
(map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
|
wenzelm@19511
|
604 |
|
wenzelm@19511
|
605 |
fun ax_arity prep =
|
wenzelm@35669
|
606 |
axiomatize (prep o ProofContext.init) Logic.mk_arities
|
wenzelm@20628
|
607 |
(map (prefix arity_prefix) o Logic.name_arities) add_arity;
|
wenzelm@19511
|
608 |
|
wenzelm@19706
|
609 |
fun class_const c =
|
wenzelm@19706
|
610 |
(Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
|
wenzelm@19706
|
611 |
|
wenzelm@19511
|
612 |
fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
|
wenzelm@19511
|
613 |
let
|
wenzelm@30344
|
614 |
val class = Sign.full_name thy bclass;
|
wenzelm@24731
|
615 |
val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
|
wenzelm@19511
|
616 |
in
|
wenzelm@19511
|
617 |
thy
|
wenzelm@19511
|
618 |
|> Sign.primitive_class (bclass, super)
|
wenzelm@19511
|
619 |
|> ax_classrel prep_classrel (map (fn c => (class, c)) super)
|
wenzelm@19706
|
620 |
|> Theory.add_deps "" (class_const class) (map class_const super)
|
wenzelm@19511
|
621 |
end;
|
wenzelm@19511
|
622 |
|
wenzelm@19511
|
623 |
in
|
wenzelm@19511
|
624 |
|
wenzelm@24929
|
625 |
val axiomatize_class = ax_class Sign.certify_class cert_classrel;
|
wenzelm@35669
|
626 |
val axiomatize_class_cmd = ax_class (ProofContext.read_class o ProofContext.init) read_classrel;
|
wenzelm@24929
|
627 |
val axiomatize_classrel = ax_classrel cert_classrel;
|
wenzelm@24929
|
628 |
val axiomatize_classrel_cmd = ax_classrel read_classrel;
|
wenzelm@35669
|
629 |
val axiomatize_arity = ax_arity ProofContext.cert_arity;
|
wenzelm@35669
|
630 |
val axiomatize_arity_cmd = ax_arity ProofContext.read_arity;
|
wenzelm@19511
|
631 |
|
wenzelm@19511
|
632 |
end;
|
wenzelm@19511
|
633 |
|
wenzelm@19511
|
634 |
end;
|