author  wenzelm 
Mon, 13 Mar 2000 12:25:52 +0100  
changeset 8420  f37fd19476ca 
parent 7351  1e485129fbc1 
child 8520  b6dd80ea3af1 
permissions  rwrr 
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(* Title: Pure/axclass.ML 
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ID: $Id$ 
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Author: Markus Wenzel, TU Muenchen 
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6379  5 
Axiomatic type class package. 
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*) 
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signature AX_CLASS = 
3938  9 
sig 
5685  10 
val quiet_mode: bool ref 
6379  11 
val print_axclasses: theory > unit 
1498  12 
val add_classrel_thms: thm list > theory > theory 
13 
val add_arity_thms: thm list > theory > theory 

6379  14 
val add_axclass: bclass * xclass list > ((bstring * string) * Args.src list) list 
15 
> theory > theory * {intro: thm, axioms: thm list} 

16 
val add_axclass_i: bclass * class list > ((bstring * term) * theory attribute list) list 

17 
> theory > theory * {intro: thm, axioms: thm list} 

3938  18 
val add_inst_subclass: xclass * xclass > string list > thm list 
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> tactic option > theory > theory 

3788  20 
val add_inst_subclass_i: class * class > string list > thm list 
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> tactic option > theory > theory 

3938  22 
val add_inst_arity: xstring * xsort list * xclass list > string list 
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> thm list > tactic option > theory > theory 

3788  24 
val add_inst_arity_i: string * sort list * class list > string list 
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> thm list > tactic option > theory > theory 

6379  26 
val axclass_tac: thm list > tactic 
1498  27 
val prove_subclass: theory > class * class > thm list 
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> tactic option > thm 

29 
val prove_arity: theory > string * sort list * class > thm list 

30 
> tactic option > thm 

3949  31 
val goal_subclass: theory > xclass * xclass > thm list 
32 
val goal_arity: theory > xstring * xsort list * xclass > thm list 

6729  33 
val instance_subclass_proof: (xclass * xclass) * Comment.text > bool > theory > ProofHistory.T 
34 
val instance_subclass_proof_i: (class * class) * Comment.text > bool > theory > ProofHistory.T 

35 
val instance_arity_proof: (xstring * xsort list * xclass) * Comment.text 

36 
> bool > theory > ProofHistory.T 

37 
val instance_arity_proof_i: (string * sort list * class) * Comment.text 

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> bool > theory > ProofHistory.T 

6379  39 
val setup: (theory > theory) list 
3938  40 
end; 
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1498  42 
structure AxClass : AX_CLASS = 
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struct 
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4015  45 

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(** utilities **) 
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5685  48 
(* messages *) 
49 

50 
val quiet_mode = ref false; 

51 
fun message s = if ! quiet_mode then () else writeln s; 

52 

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(* type vars *) 
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fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys) 
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 map_typ_frees f (TFree a) = f a 
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 map_typ_frees _ a = a; 
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val map_term_tfrees = map_term_types o map_typ_frees; 
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fun aT S = TFree ("'a", S); 
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3395  64 
fun dest_varT (TFree (x, S)) = ((x, ~1), S) 
65 
 dest_varT (TVar xi_S) = xi_S 

3788  66 
 dest_varT T = raise TYPE ("dest_varT", [T], []); 
3395  67 

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(* get axioms and theorems *) 
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1498  71 
val is_def = Logic.is_equals o #prop o rep_thm; 
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4934  73 
fun witnesses thy names thms = 
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PureThy.get_thmss thy names @ thms @ filter is_def (map snd (axioms_of thy)); 
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560  78 
(** abstract syntax operations **) 
423  79 

6379  80 
(* names *) 
81 

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fun intro_name c = c ^ "I"; 

83 
val introN = "intro"; 

84 
val axiomsN = "axioms"; 

85 

86 

423  87 
(* subclass relations as terms *) 
88 

1498  89 
fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2); 
423  90 

91 
fun dest_classrel tm = 

92 
let 

3788  93 
fun err () = raise TERM ("dest_classrel", [tm]); 
423  94 

3395  95 
val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err (); 
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val c1 = (case dest_varT ty of (_, [c]) => c  _ => err ()) 

97 
handle TYPE _ => err (); 

6379  98 
in (c1, c2) end; 
423  99 

100 

101 
(* arities as terms *) 

102 

103 
fun mk_arity (t, ss, c) = 

104 
let 

449  105 
val names = tl (variantlist (replicate (length ss + 1) "'", [])); 
2266  106 
val tfrees = ListPair.map TFree (names, ss); 
6379  107 
in Logic.mk_inclass (Type (t, tfrees), c) end; 
423  108 

109 
fun dest_arity tm = 

110 
let 

3788  111 
fun err () = raise TERM ("dest_arity", [tm]); 
423  112 

3395  113 
val (ty, c) = Logic.dest_inclass tm handle TERM _ => err (); 
114 
val (t, tvars) = 

423  115 
(case ty of 
3395  116 
Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ()) 
423  117 
 _ => err ()); 
118 
val ss = 

3395  119 
if null (gen_duplicates eq_fst tvars) 
120 
then map snd tvars else err (); 

6379  121 
in (t, ss, c) end; 
423  122 

123 

124 

560  125 
(** add theorems as axioms **) 
423  126 

127 
fun prep_thm_axm thy thm = 

128 
let 

129 
fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]); 

130 

1237  131 
val {sign, hyps, prop, ...} = rep_thm thm; 
423  132 
in 
6390  133 
if not (Sign.subsig (sign, Theory.sign_of thy)) then 
423  134 
err "theorem not of same theory" 
1237  135 
else if not (null (extra_shyps thm)) orelse not (null hyps) then 
423  136 
err "theorem may not contain hypotheses" 
137 
else prop 

138 
end; 

139 

140 
(*theorems expressing class relations*) 

141 
fun add_classrel_thms thms thy = 

142 
let 

143 
fun prep_thm thm = 

144 
let 

145 
val prop = prep_thm_axm thy thm; 

146 
val (c1, c2) = dest_classrel prop handle TERM _ => 

147 
raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]); 

148 
in (c1, c2) end; 

6379  149 
in Theory.add_classrel (map prep_thm thms) thy end; 
423  150 

151 
(*theorems expressing arities*) 

152 
fun add_arity_thms thms thy = 

153 
let 

154 
fun prep_thm thm = 

155 
let 

156 
val prop = prep_thm_axm thy thm; 

157 
val (t, ss, c) = dest_arity prop handle TERM _ => 

158 
raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]); 

159 
in (t, ss, [c]) end; 

6379  160 
in Theory.add_arities (map prep_thm thms) thy end; 
161 

162 

163 

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(** axclass info **) 

165 

166 
(* data kind 'Pure/axclasses' *) 

167 

168 
type axclass_info = 

169 
{super_classes: class list, 

170 
intro: thm, 

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axioms: thm list}; 

172 

173 
structure AxclassesArgs = 

174 
struct 

175 
val name = "Pure/axclasses"; 

176 
type T = axclass_info Symtab.table; 

177 

178 
val empty = Symtab.empty; 

6546  179 
val copy = I; 
6379  180 
val prep_ext = I; 
181 
fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2); 

182 

183 
fun print sg tab = 

184 
let 

185 
val ext_class = Sign.cond_extern sg Sign.classK; 

186 
val ext_thm = PureThy.cond_extern_thm_sg sg; 

187 

188 
fun pretty_class c cs = Pretty.block 

189 
(Pretty.str (ext_class c) :: Pretty.str " <" :: Pretty.brk 1 :: 

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Pretty.breaks (map (Pretty.str o ext_class) cs)); 

191 

192 
fun pretty_thms name thms = Pretty.big_list (name ^ ":") (map Display.pretty_thm thms); 

193 

194 
fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks 

195 
[pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]); 

196 
in seq (Pretty.writeln o pretty_axclass) (Symtab.dest tab) end; 

197 
end; 

198 

199 
structure AxclassesData = TheoryDataFun(AxclassesArgs); 

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val print_axclasses = AxclassesData.print; 

201 

202 

203 
(* get and put data *) 

204 

205 
fun lookup_axclass_info_sg sg c = Symtab.lookup (AxclassesData.get_sg sg, c); 

206 

207 
fun get_axclass_info thy c = 

208 
(case lookup_axclass_info_sg (Theory.sign_of thy) c of 

209 
None => error ("Unknown axclass " ^ quote c) 

210 
 Some info => info); 

211 

212 
fun put_axclass_info c info thy = 

213 
thy > AxclassesData.put (Symtab.update ((c, info), AxclassesData.get thy)); 

423  214 

215 

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(** add axiomatic type classes **) 

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(* errors *) 
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fun err_not_logic c = 
4917  222 
error ("Axiomatic class " ^ quote c ^ " not subclass of " ^ quote logicC); 
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fun err_bad_axsort ax c = 
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error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c); 
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fun err_bad_tfrees ax = 
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error ("More than one type variable in axiom " ^ quote ax); 
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(* ext_axclass *) 
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6379  233 
fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy = 
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let 
6379  235 
val sign = Theory.sign_of thy; 
3938  236 

6379  237 
val class = Sign.full_name sign bclass; 
238 
val super_classes = map (prep_class sign) raw_super_classes; 

239 
val axms = map (prep_axm sign o fst) raw_axioms_atts; 

240 
val atts = map (map (prep_att thy) o snd) raw_axioms_atts; 

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6379  242 
(*declare class*) 
243 
val class_thy = 

244 
thy > Theory.add_classes_i [(bclass, super_classes)]; 

245 
val class_sign = Theory.sign_of class_thy; 

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6379  247 
(*prepare abstract axioms*) 
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fun abs_axm ax = 
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if null (term_tfrees ax) then 
1498  250 
Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax) 
3788  251 
else map_term_tfrees (K (aT [class])) ax; 
6379  252 
val abs_axms = map (abs_axm o #2) axms; 
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6379  254 
(*prepare introduction rule*) 
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val _ = if Sign.subsort class_sign ([class], logicS) then () else err_not_logic class; 

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fun axm_sort (name, ax) = 
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(case term_tfrees ax of 
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[] => [] 
6379  260 
 [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class 
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 _ => err_bad_tfrees name); 
6379  262 
val axS = Sign.norm_sort class_sign (logicC :: flat (map axm_sort axms)); 
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1498  264 
val int_axm = Logic.close_form o map_term_tfrees (K (aT axS)); 
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fun inclass c = Logic.mk_inclass (aT axS, c); 

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1498  267 
val intro_axm = Logic.list_implies 
6379  268 
(map inclass super_classes @ map (int_axm o #2) axms, inclass class); 
269 

270 
(*declare axioms and rule*) 

8420  271 
val (axms_thy, ([intro], [axioms])) = 
6379  272 
class_thy 
273 
> Theory.add_path bclass 

274 
> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)] 

8420  275 
>>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; 
6379  276 
val info = {super_classes = super_classes, intro = intro, axioms = axioms}; 
277 

278 
(*store info*) 

279 
val final_thy = 

280 
axms_thy 

8420  281 
> (#1 o PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)) 
6379  282 
> Theory.parent_path 
8420  283 
> (#1 o PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)]) 
6379  284 
> put_axclass_info class info; 
285 
in (final_thy, {intro = intro, axioms = axioms}) end; 

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(* external interfaces *) 
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6390  290 
val add_axclass = ext_axclass Sign.intern_class Theory.read_axm Attrib.global_attribute; 
291 
val add_axclass_i = ext_axclass (K I) Theory.cert_axm (K I); 

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423  295 
(** prove class relations and type arities **) 
296 

297 
(* class_axms *) 

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6379  299 
fun class_axms sign = 
300 
let val classes = Sign.classes sign in 

301 
map (Thm.class_triv sign) classes @ 

302 
mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes 

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end; 
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423  305 

7351  306 
(* intro_classes *) 
6379  307 

7351  308 
fun intro_classes_tac st = 
6379  309 
TRY (REPEAT_FIRST (resolve_tac (class_axms (Thm.sign_of_thm st)))) st; 
310 

7351  311 
val intro_classes_method = 
312 
("intro_classes", Method.no_args (Method.METHOD0 intro_classes_tac), 

313 
"backchain introduction rules of axiomatic type classes"); 

6379  314 

315 

423  316 
(* axclass_tac *) 
317 

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(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", 
1217  319 
try class_trivs first, then "cI" axioms 
423  320 
(2) rewrite goals using user supplied definitions 
321 
(3) repeatedly resolve goals with user supplied nondefinitions*) 

322 

6379  323 
fun axclass_tac thms = 
1217  324 
let 
325 
val defs = filter is_def thms; 

326 
val non_defs = filter_out is_def thms; 

327 
in 

7351  328 
intro_classes_tac THEN 
1217  329 
TRY (rewrite_goals_tac defs) THEN 
330 
TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i)) 

331 
end; 

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423  334 
(* provers *) 
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6379  336 
fun prove mk_prop str_of thy sig_prop thms usr_tac = 
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let 
6390  338 
val sign = Theory.sign_of thy; 
6679  339 
val goal = Thm.cterm_of sign (mk_prop sig_prop) 
340 
handle TERM (msg, _) => error msg 

341 
 TYPE (msg, _, _) => error msg; 

6379  342 
val tac = axclass_tac thms THEN (if_none usr_tac all_tac); 
423  343 
in 
344 
prove_goalw_cterm [] goal (K [tac]) 

345 
end 

346 
handle ERROR => error ("The error(s) above occurred while trying to prove " 

6390  347 
^ quote (str_of (Theory.sign_of thy, sig_prop))); 
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638  349 
val prove_subclass = 
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uses Sign.str_of_classrel, Sign.str_of_arity, Sign.str_of_arity;
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prove mk_classrel (fn (sg, c1_c2) => Sign.str_of_classrel sg c1_c2); 
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axiomatic type class 'package' for Pure (alpha version);
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351 

423  352 
val prove_arity = 
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uses Sign.str_of_classrel, Sign.str_of_arity, Sign.str_of_arity;
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prove mk_arity (fn (sg, (t, Ss, c)) => Sign.str_of_arity sg (t, Ss, [c])); 
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axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
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354 

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axiomatic type class 'package' for Pure (alpha version);
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355 

423  356 

449  357 
(** add proved subclass relations and arities **) 
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3949  359 
fun intrn_classrel sg c1_c2 = 
360 
pairself (Sign.intern_class sg) c1_c2; 

361 

6379  362 
fun intrn_arity intrn sg (t, Ss, x) = 
363 
(Sign.intern_tycon sg t, map (Sign.intern_sort sg) Ss, intrn sg x); 

364 

365 

366 
fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy = 

367 
let val c1_c2 = prep_classrel (Theory.sign_of thy) raw_c1_c2 in 

5685  368 
message ("Proving class inclusion " ^ 
6390  369 
quote (Sign.str_of_classrel (Theory.sign_of thy) c1_c2) ^ " ..."); 
6379  370 
thy > add_classrel_thms [prove_subclass thy c1_c2 (witnesses thy names thms) usr_tac] 
3788  371 
end; 
423  372 

6379  373 
fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy = 
423  374 
let 
6379  375 
val sign = Theory.sign_of thy; 
376 
val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs); 

4934  377 
val wthms = witnesses thy names thms; 
423  378 
fun prove c = 
5685  379 
(message ("Proving type arity " ^ 
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quote (Sign.str_of_arity sign (t, Ss, [c])) ^ " ..."); 
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uses Sign.str_of_classrel, Sign.str_of_arity, Sign.str_of_arity;
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prove_arity thy (t, Ss, c) wthms usr_tac); 
6379  382 
in add_arity_thms (map prove cs) thy end; 
383 

384 

385 
val add_inst_subclass = ext_inst_subclass intrn_classrel; 

386 
val add_inst_subclass_i = ext_inst_subclass (K I); 

387 
val add_inst_arity = ext_inst_arity (intrn_arity Sign.intern_sort); 

388 
val add_inst_arity_i = ext_inst_arity (K I); 

389 

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390 

6379  391 
(* make oldstyle interactive goals *) 
392 

393 
fun mk_goal mk_prop thy sig_prop = 

394 
Goals.goalw_cterm [] (Thm.cterm_of (Theory.sign_of thy) (mk_prop (Theory.sign_of thy) sig_prop)); 

395 

396 
val goal_subclass = mk_goal (mk_classrel oo intrn_classrel); 

397 
val goal_arity = mk_goal (mk_arity oo intrn_arity Sign.intern_class); 

398 

3788  399 

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400 

6379  401 
(** instance proof interfaces **) 
402 

403 
fun inst_attribute add_thms (thy, thm) = (add_thms [thm] thy, thm); 

404 

6729  405 
fun inst_proof mk_prop add_thms (sig_prop, comment) int thy = 
6379  406 
thy 
6729  407 
> IsarThy.theorem_i (("", [inst_attribute add_thms], 
6935  408 
(mk_prop (Theory.sign_of thy) sig_prop, ([], []))), comment) int; 
3949  409 

6379  410 
val instance_subclass_proof = inst_proof (mk_classrel oo intrn_classrel) add_classrel_thms; 
411 
val instance_subclass_proof_i = inst_proof (K mk_classrel) add_classrel_thms; 

412 
val instance_arity_proof = inst_proof (mk_arity oo intrn_arity Sign.intern_class) add_arity_thms; 

413 
val instance_arity_proof_i = inst_proof (K mk_arity) add_arity_thms; 

414 

415 

416 

417 
(** package setup **) 

418 

419 
(* setup theory *) 

3949  420 

6379  421 
val setup = 
422 
[AxclassesData.init, 

7351  423 
Method.add_methods [intro_classes_method]]; 
6379  424 

425 

426 
(* outer syntax *) 

427 

6719  428 
local structure P = OuterParse and K = OuterSyntax.Keyword in 
3949  429 

6379  430 
val axclassP = 
6719  431 
OuterSyntax.command "axclass" "define axiomatic type class" K.thy_decl 
6729  432 
(((P.name  Scan.optional (P.$$$ "<"  P.!!! (P.list1 P.xname)) [])  P.marg_comment) 
433 
 Scan.repeat (P.spec_name  P.marg_comment) 

6379  434 
>> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs))); 
435 

436 
val instanceP = 

6719  437 
OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal 
6729  438 
((P.xname  (P.$$$ "<"  P.xname)  P.marg_comment >> instance_subclass_proof  
439 
(P.xname  (P.$$$ "::"  P.simple_arity) >> P.triple2)  P.marg_comment 

440 
>> instance_arity_proof) 

6379  441 
>> (Toplevel.print oo Toplevel.theory_to_proof)); 
442 

443 
val _ = OuterSyntax.add_parsers [axclassP, instanceP]; 

444 

445 
end; 

3949  446 

447 

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axiomatic type class 'package' for Pure (alpha version);
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parents:
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448 
end; 