author  wenzelm 
Thu, 21 Apr 2005 22:02:06 +0200  
changeset 15801  d2f5ca3c048d 
parent 15705  b5edb9dcec9a 
child 15853  68b615bc110e 
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 
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val print_axclasses: theory > unit 
1498  12 
val add_classrel_thms: thm list > theory > theory 
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val add_arity_thms: thm list > theory > theory 

15703  14 
val add_axclass: bclass * xclass list > ((bstring * string) * Attrib.src list) list 
6379  15 
> theory > theory * {intro: thm, axioms: thm list} 
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val add_axclass_i: bclass * class list > ((bstring * term) * theory attribute list) list 

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

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val add_inst_subclass_x: xclass * xclass > string list > thm list 
3788  19 
> tactic option > theory > theory 
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val add_inst_subclass: xclass * xclass > tactic > theory > theory 
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val add_inst_subclass_i: class * class > tactic > theory > theory 

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val add_inst_arity_x: xstring * string list * string > string list 

3938  23 
> thm list > tactic option > theory > theory 
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val add_inst_arity: xstring * string list * string > tactic > theory > theory 
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val add_inst_arity_i: string * sort list * sort > tactic > theory > theory 

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val default_intro_classes_tac: thm list > tactic 
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val axclass_tac: thm list > tactic 
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val instance_subclass_proof: xclass * xclass > bool > theory > ProofHistory.T 
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val instance_subclass_proof_i: class * class > bool > theory > ProofHistory.T 
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val instance_arity_proof: xstring * string list * string > bool > theory > ProofHistory.T 
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val instance_arity_proof_i: string * sort list * sort > bool > theory > ProofHistory.T 
3938  32 
end; 
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15801  34 
structure AxClass: AX_CLASS = 
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struct 
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4015  37 

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(** utilities **) 
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5685  40 
(* messages *) 
41 

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val quiet_mode = ref false; 

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

44 

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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  56 
fun dest_varT (TFree (x, S)) = ((x, ~1), S) 
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 dest_varT (TVar xi_S) = xi_S 

3788  58 
 dest_varT T = raise TYPE ("dest_varT", [T], []); 
3395  59 

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(* get axioms and theorems *) 
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val is_def = Logic.is_equals o #prop o rep_thm; 
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4934  65 
fun witnesses thy names thms = 
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PureThy.get_thmss thy (map (rpair NONE) names) @ thms @ List.filter is_def (map snd (axioms_of thy)); 
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560  70 
(** abstract syntax operations **) 
423  71 

6379  72 
(* names *) 
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fun intro_name c = c ^ "I"; 

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val introN = "intro"; 

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val axiomsN = "axioms"; 

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(* subclass relations as terms *) 
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fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2); 
423  82 

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fun dest_classrel tm = 

84 
let 

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fun err () = raise TERM ("dest_classrel", [tm]); 
423  86 

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

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handle TYPE _ => err (); 

6379  90 
in (c1, c2) end; 
423  91 

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(* arities as terms *) 

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fun mk_arity (t, Ss, c) = 
423  96 
let 
14695  97 
val tfrees = ListPair.map TFree (Term.invent_names [] "'a" (length Ss), Ss); 
6379  98 
in Logic.mk_inclass (Type (t, tfrees), c) end; 
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fun mk_arities (t, Ss, S) = map (fn c => mk_arity (t, Ss, c)) S; 
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fun dest_arity tm = 
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let 

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fun err () = raise TERM ("dest_arity", [tm]); 
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3395  106 
val (ty, c) = Logic.dest_inclass tm handle TERM _ => err (); 
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val (t, tvars) = 

423  108 
(case ty of 
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Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ()) 
423  110 
 _ => err ()); 
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val ss = 

3395  112 
if null (gen_duplicates eq_fst tvars) 
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then map snd tvars else err (); 

6379  114 
in (t, ss, c) end; 
423  115 

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560  118 
(** add theorems as axioms **) 
423  119 

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fun prep_thm_axm thy thm = 

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let 

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

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val {sign, hyps, prop, ...} = rep_thm thm; 
423  125 
in 
6390  126 
if not (Sign.subsig (sign, Theory.sign_of thy)) then 
423  127 
err "theorem not of same theory" 
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else if not (null (extra_shyps thm)) orelse not (null hyps) then 
423  129 
err "theorem may not contain hypotheses" 
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else prop 

131 
end; 

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(*theorems expressing class relations*) 

134 
fun add_classrel_thms thms thy = 

135 
let 

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fun prep_thm thm = 

137 
let 

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val prop = prep_thm_axm thy thm; 

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

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

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in (c1, c2) end; 

8897  142 
in Theory.add_classrel_i (map prep_thm thms) thy end; 
423  143 

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(*theorems expressing arities*) 

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fun add_arity_thms thms thy = 

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let 

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fun prep_thm thm = 

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let 

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val prop = prep_thm_axm thy thm; 

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

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

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

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in Theory.add_arities_i (map prep_thm thms) thy end; 
6379  154 

155 

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(** axclass info **) 

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(* data kind 'Pure/axclasses' *) 

160 

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type axclass_info = 

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{super_classes: class list, 

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intro: thm, 

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axioms: thm list}; 

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structure AxclassesArgs = 

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struct 

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val name = "Pure/axclasses"; 

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type T = axclass_info Symtab.table; 

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val empty = Symtab.empty; 

6546  172 
val copy = I; 
6379  173 
val prep_ext = I; 
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fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2); 

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fun print sg tab = 

177 
let 

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val ext_class = Sign.cond_extern sg Sign.classK; 

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val ext_thm = PureThy.cond_extern_thm_sg sg; 

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181 
fun pretty_class c cs = Pretty.block 

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

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

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10008  185 
fun pretty_thms name thms = Pretty.big_list (name ^ ":") 
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(map (Display.pretty_thm_sg sg) thms); 

6379  187 

188 
fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks 

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

8720  190 
in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest tab))) end; 
6379  191 
end; 
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193 
structure AxclassesData = TheoryDataFun(AxclassesArgs); 

15801  194 
val _ = Context.add_setup [AxclassesData.init]; 
6379  195 
val print_axclasses = AxclassesData.print; 
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197 

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(* get and put data *) 

199 

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

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202 
fun get_axclass_info thy c = 

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(case lookup_axclass_info_sg (Theory.sign_of thy) c of 

15531  204 
NONE => error ("Unknown axclass " ^ quote c) 
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 SOME info => info); 

6379  206 

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fun put_axclass_info c info thy = 

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

423  209 

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(** add axiomatic type classes **) 

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(* errors *) 
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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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fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy = 
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let 
6379  227 
val sign = Theory.sign_of thy; 
3938  228 

6379  229 
val class = Sign.full_name sign bclass; 
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val super_classes = map (prep_class sign) raw_super_classes; 

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

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

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6379  234 
(*declare class*) 
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val class_thy = 

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

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val class_sign = Theory.sign_of class_thy; 

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(*prepare abstract axioms*) 
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fun abs_axm ax = 
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if null (term_tfrees ax) then 
14854  242 
Logic.mk_implies (Logic.mk_inclass (aT [], class), ax) 
3788  243 
else map_term_tfrees (K (aT [class])) ax; 
6379  244 
val abs_axms = map (abs_axm o #2) axms; 
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fun axm_sort (name, ax) = 
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(case term_tfrees ax of 
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[] => [] 
6379  249 
 [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class 
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 _ => err_bad_tfrees name); 
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val axS = Sign.certify_sort class_sign (List.concat (map axm_sort axms)); 
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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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val intro_axm = Logic.list_implies 
6379  257 
(map inclass super_classes @ map (int_axm o #2) axms, inclass class); 
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259 
(*declare axioms and rule*) 

8420  260 
val (axms_thy, ([intro], [axioms])) = 
6379  261 
class_thy 
262 
> Theory.add_path bclass 

263 
> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)] 

8420  264 
>>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; 
6379  265 
val info = {super_classes = super_classes, intro = intro, axioms = axioms}; 
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267 
(*store info*) 

268 
val final_thy = 

269 
axms_thy 

8420  270 
> (#1 o PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)) 
6379  271 
> Theory.parent_path 
8420  272 
> (#1 o PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)]) 
6379  273 
> put_axclass_info class info; 
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in (final_thy, {intro = intro, axioms = axioms}) end; 

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(* external interfaces *) 
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6390  279 
val add_axclass = ext_axclass Sign.intern_class Theory.read_axm Attrib.global_attribute; 
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val add_axclass_i = ext_axclass (K I) Theory.cert_axm (K I); 

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(** prove class relations and type arities **) 
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286 
(* class_axms *) 

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6379  288 
fun class_axms sign = 
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let val classes = Sign.classes sign in 

290 
map (Thm.class_triv sign) classes @ 

15570  291 
List.mapPartial (Option.map #intro o lookup_axclass_info_sg sign) classes 
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end; 
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423  294 

15801  295 
(* proof methods *) 
6379  296 

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fun intro_classes_tac facts st = 
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(ALLGOALS (Method.insert_tac facts THEN' 
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REPEAT_ALL_NEW (resolve_tac (class_axms (Thm.sign_of_thm st)))) 
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THEN Tactic.distinct_subgoals_tac) st; 
6379  301 

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fun default_intro_classes_tac [] = intro_classes_tac [] 
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 default_intro_classes_tac _ = Tactical.no_tac; (*no error message!*) 
10309  304 

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fun default_tac rules ctxt facts = 

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HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE 
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default_intro_classes_tac facts; 
10309  308 

15801  309 
val _ = Context.add_setup [Method.add_methods 
310 
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac), 

311 
"backchain introduction rules of axiomatic type classes"), 

312 
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule")]]; 

10309  313 

314 

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(* oldstyle axclass_tac *) 
423  316 

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(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", 
1217  318 
try class_trivs first, then "cI" axioms 
423  319 
(2) rewrite goals using user supplied definitions 
320 
(3) repeatedly resolve goals with user supplied nondefinitions*) 

321 

6379  322 
fun axclass_tac thms = 
1217  323 
let 
15570  324 
val defs = List.filter is_def thms; 
1217  325 
val non_defs = filter_out is_def thms; 
326 
in 

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

330 
end; 

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332 

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(* oldstyle provers *) 
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11969  335 
fun prove mk_prop str_of sign prop thms usr_tac = 
15570  336 
(Tactic.prove sign [] [] (mk_prop prop) (K (axclass_tac thms THEN (getOpt (usr_tac,all_tac)))) 
11969  337 
handle ERROR => error ("The error(s) above occurred while trying to prove " ^ 
338 
quote (str_of sign prop))) > Drule.standard; 

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14824  340 
val prove_subclass = prove mk_classrel (fn sg => fn (c1, c2) => 
341 
Pretty.string_of_classrel (Sign.pp sg) [c1, c2]); 

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14824  343 
val prove_arity = prove mk_arity (fn sg => fn (t, Ss, c) => 
344 
Pretty.string_of_arity (Sign.pp sg) (t, Ss, [c])); 

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345 

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423  347 

449  348 
(** add proved subclass relations and arities **) 
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8897  350 
(* prepare classes and arities *) 
351 

352 
fun read_class sg c = Sign.certify_class sg (Sign.intern_class sg c); 

353 

14824  354 
fun test_classrel sg cc = (Type.add_classrel (Sign.pp sg) [cc] (Sign.tsig_of sg); cc); 
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fun cert_classrel sg = test_classrel sg o Library.pairself (Sign.certify_class sg); 
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fun read_classrel sg = test_classrel sg o Library.pairself (read_class sg); 
3949  357 

14824  358 
fun test_arity sg ar = (Type.add_arities (Sign.pp sg) [ar] (Sign.tsig_of sg); ar); 
6379  359 

8897  360 
fun prep_arity prep_tycon prep_sort prep_x sg (t, Ss, x) = 
14824  361 
test_arity sg (prep_tycon sg t, map (prep_sort sg) Ss, prep_x sg x); 
8897  362 

363 
val read_arity = prep_arity Sign.intern_tycon Sign.read_sort Sign.read_sort; 

364 
val cert_arity = prep_arity (K I) Sign.certify_sort Sign.certify_sort; 

365 

366 

367 
(* oldstyle instance declarations *) 

6379  368 

369 
fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy = 

11969  370 
let 
371 
val sign = Theory.sign_of thy; 

14824  372 
val (c1, c2) = prep_classrel sign raw_c1_c2; 
11969  373 
in 
14824  374 
message ("Proving class inclusion " ^ quote (Sign.string_of_classrel sign [c1, c2]) ^ " ..."); 
375 
thy > add_classrel_thms [prove_subclass sign (c1, c2) (witnesses thy names thms) usr_tac] 

3788  376 
end; 
423  377 

6379  378 
fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy = 
423  379 
let 
6379  380 
val sign = Theory.sign_of thy; 
381 
val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs); 

4934  382 
val wthms = witnesses thy names thms; 
423  383 
fun prove c = 
5685  384 
(message ("Proving type arity " ^ 
14824  385 
quote (Sign.string_of_arity sign (t, Ss, [c])) ^ " ..."); 
11969  386 
prove_arity sign (t, Ss, c) wthms usr_tac); 
6379  387 
in add_arity_thms (map prove cs) thy end; 
388 

15531  389 
fun sane_inst_subclass prep sub tac = ext_inst_subclass prep sub [] [] (SOME tac); 
390 
fun sane_inst_arity prep arity tac = ext_inst_arity prep arity [] [] (SOME tac); 

6379  391 

11828  392 
val add_inst_subclass_x = ext_inst_subclass read_classrel; 
393 
val add_inst_subclass = sane_inst_subclass read_classrel; 

394 
val add_inst_subclass_i = sane_inst_subclass cert_classrel; 

395 
val add_inst_arity_x = ext_inst_arity read_arity; 

396 
val add_inst_arity = sane_inst_arity read_arity; 

397 
val add_inst_arity_i = sane_inst_arity cert_arity; 

6379  398 

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

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fun inst_proof mk_prop add_thms inst int theory = 
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theory 
15696  405 
> IsarThy.multi_theorem_i Drule.internalK I ProofContext.export_standard 
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("", [fn (thy, th) => (add_thms [th] thy, th)]) [] 
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(map (fn t => (("", []), [(t, ([], []))])) (mk_prop (Theory.sign_of theory) inst)) int; 
6379  408 

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val instance_subclass_proof = 
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inst_proof (single oo (mk_classrel oo read_classrel)) add_classrel_thms; 
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val instance_subclass_proof_i = 
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inst_proof (single oo (mk_classrel oo cert_classrel)) add_classrel_thms; 
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val instance_arity_proof = inst_proof (mk_arities oo read_arity) add_arity_thms; 
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val instance_arity_proof_i = inst_proof (mk_arities oo cert_arity) add_arity_thms; 
6379  415 

416 

417 
(* outer syntax *) 

418 

6719  419 
local structure P = OuterParse and K = OuterSyntax.Keyword in 
3949  420 

6379  421 
val axclassP = 
6719  422 
OuterSyntax.command "axclass" "define axiomatic type class" K.thy_decl 
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((P.name  Scan.optional ((P.$$$ "\\<subseteq>"  P.$$$ "<")  
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P.!!! (P.list1 P.xname)) [])  Scan.repeat P.spec_name 
6379  425 
>> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs))); 
426 

427 
val instanceP = 

6719  428 
OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal 
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((P.xname  ((P.$$$ "\\<subseteq>"  P.$$$ "<")  P.xname) >> instance_subclass_proof  
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(P.xname  (P.$$$ "::"  P.arity) >> P.triple2) >> instance_arity_proof) 
6379  431 
>> (Toplevel.print oo Toplevel.theory_to_proof)); 
432 

433 
val _ = OuterSyntax.add_parsers [axclassP, instanceP]; 

434 

435 
end; 

3949  436 

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end; 