author  wenzelm 
Tue, 31 May 2005 11:53:13 +0200  
changeset 16122  864fda4a4056 
parent 15973  5fd94d84470f 
child 16180  a51be5cbd81d 
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 = 
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sig 
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val quiet_mode: bool ref 
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val print_axclasses: theory > unit 
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val add_axclass: bclass * xclass list > ((bstring * string) * Attrib.src list) list 
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> 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_classrel_thms: thm list > theory > theory 
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val add_arity_thms: thm list > 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: 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 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 
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val intro_classes_tac: thm list > tactic 
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val default_intro_classes_tac: thm list > tactic 
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(*legacy interfaces*) 
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val axclass_tac: thm list > tactic 
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val add_inst_subclass_x: xclass * xclass > string list > thm list 
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> tactic option > theory > theory 
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val add_inst_arity_x: xstring * string list * string > string list 
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> thm list > tactic option > theory > theory 
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end; 
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structure AxClass: AX_CLASS = 
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struct 
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4015  40 

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(** utilities **) 
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(* messages *) 
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val quiet_mode = ref false; 

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

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

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 dest_varT T = raise TYPE ("dest_varT", [T], []); 
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(** abstract syntax operations **) 
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(* 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); 
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fun dest_classrel tm = 

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let 

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

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in (c1, c2) end; 
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(* arities as terms *) 

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fun mk_arity (t, Ss, c) = 
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let 
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val tfrees = ListPair.map TFree (Term.invent_names [] "'a" (length Ss), Ss); 
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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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val (ty, c) = Logic.dest_inclass tm handle TERM _ => err (); 
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val (t, tvars) = 

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

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

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in (t, ss, c) end; 
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(** axclass info **) 
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(* data kind 'Pure/axclasses' *) 

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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; 

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val copy = I; 
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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 = 

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let 

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val ext_class = Sign.extern sg Sign.classK; 
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val ext_thm = PureThy.extern_thm_sg sg; 

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

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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]); 

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in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest tab))) end; 
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end; 
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structure AxclassesData = TheoryDataFun(AxclassesArgs); 

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val _ = Context.add_setup [AxclassesData.init]; 
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val print_axclasses = AxclassesData.print; 
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(* get and put data *) 

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

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fun get_axclass_info thy c = 

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(case lookup_axclass_info_sg (Theory.sign_of thy) c of 

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

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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)); 

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(* class_axms *) 
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fun class_axms sign = 
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let val classes = Sign.classes sign in 
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map (Thm.class_triv sign) classes @ 
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List.mapPartial (Option.map #intro o lookup_axclass_info_sg sign) classes 
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end; 
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(** add axiomatic type classes **) 

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local 
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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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fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy = 
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let 
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val sign = Theory.sign_of thy; 
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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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(*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 
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Logic.mk_implies (Logic.mk_inclass (aT [], class), ax) 
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else map_term_tfrees (K (aT [class])) ax; 
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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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[] => [] 
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 [(_, 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 
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(map inclass super_classes @ map (int_axm o #2) axms, inclass class); 
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(*declare axioms and rule*) 

8420  222 
val (axms_thy, ([intro], [axioms])) = 
6379  223 
class_thy 
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> Theory.add_path bclass 

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

8420  226 
>>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; 
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val info = {super_classes = super_classes, intro = intro, axioms = axioms}; 
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(*store info*) 

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val final_thy = 

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axms_thy 

8420  232 
> (#1 o PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)) 
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> Theory.parent_path 
8420  234 
> (#1 o PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)]) 
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> put_axclass_info class info; 
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in (final_thy, {intro = intro, axioms = axioms}) end; 

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in 
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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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end; 
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(** proven class instantiation **) 
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(* add thms to type signature *) 
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fun add_classrel_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 = Drule.plain_prop_of (Thm.transfer thy thm); 
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val (c1, c2) = dest_classrel prop handle TERM _ => 
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raise THM ("add_classrel_thms: not a class relation", 0, [thm]); 
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in (c1, c2) end; 
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in Theory.add_classrel_i (map prep_thm thms) thy end; 
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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 = Drule.plain_prop_of (Thm.transfer thy thm); 
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val (t, ss, c) = dest_arity prop handle TERM _ => 
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raise THM ("add_arity_thms: 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; 
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270 

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(* prepare classes and arities *) 
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fun read_class sg c = Sign.certify_class sg (Sign.intern_class sg c); 
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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); 
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fun test_arity sg ar = (Type.add_arities (Sign.pp sg) [ar] (Sign.tsig_of sg); ar); 
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281 

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fun prep_arity prep_tycon prep_sort prep sg (t, Ss, x) = 
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test_arity sg (prep_tycon sg t, map (prep_sort sg) Ss, prep sg x); 
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val read_arity = prep_arity Sign.intern_tycon Sign.read_sort Sign.read_sort; 
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val cert_arity = prep_arity (K I) Sign.certify_sort Sign.certify_sort; 
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(* instance declarations  tactical proof *) 
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local 
423  292 

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fun ext_inst_subclass prep_classrel raw_cc tac thy = 
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let 
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val sign = Theory.sign_of thy; 
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val (c1, c2) = prep_classrel sign raw_cc; 
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val txt = quote (Sign.string_of_classrel sign [c1, c2]); 
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val _ = message ("Proving class inclusion " ^ txt ^ " ..."); 
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val th = Tactic.prove sign [] [] (mk_classrel (c1, c2)) (K tac) handle ERROR => 
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error ("The error(s) above occurred while trying to prove " ^ txt); 
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in add_classrel_thms [th] thy end; 
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fun ext_inst_arity prep_arity raw_arity tac thy = 
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let 
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val sign = Theory.sign_of thy; 
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val arity = prep_arity sign raw_arity; 
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val txt = quote (Sign.string_of_arity sign arity); 
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val _ = message ("Proving type arity " ^ txt ^ " ..."); 
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val props = (mk_arities arity); 
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val ths = Tactic.prove_multi sign [] [] props 
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(fn _ => Tactic.smart_conjunction_tac (length props) THEN tac) 
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handle ERROR => error ("The error(s) above occurred while trying to prove " ^ txt); 
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in add_arity_thms ths thy end; 
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314 

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in 
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316 

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val add_inst_subclass = ext_inst_subclass read_classrel; 
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val add_inst_subclass_i = ext_inst_subclass cert_classrel; 
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val add_inst_arity = ext_inst_arity read_arity; 
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val add_inst_arity_i = ext_inst_arity cert_arity; 
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321 

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end; 
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323 

423  324 

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(* instance declarations  Isar proof *) 
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326 

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local 
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328 

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fun inst_proof mk_prop add_thms inst int theory = 
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theory 
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> 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; 
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334 

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335 
in 
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336 

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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; 
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343 

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344 
end; 
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345 

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346 

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(* tactics and methods *) 
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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  353 

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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  356 

357 
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  360 

15801  361 
val _ = Context.add_setup [Method.add_methods 
362 
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac), 

363 
"backchain introduction rules of axiomatic type classes"), 

364 
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule")]]; 

10309  365 

366 

423  367 

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(** outer syntax **) 
6379  369 

6719  370 
local structure P = OuterParse and K = OuterSyntax.Keyword in 
3949  371 

6379  372 
val axclassP = 
6719  373 
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  376 
>> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs))); 
377 

378 
val instanceP = 

6719  379 
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  382 
>> (Toplevel.print oo Toplevel.theory_to_proof)); 
383 

384 
val _ = OuterSyntax.add_parsers [axclassP, instanceP]; 

385 

386 
end; 

3949  387 

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388 

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389 

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(** oldstyle instantiation proofs **) 
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391 

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(* axclass_tac *) 
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393 

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(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", 
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try class_trivs first, then "cI" axioms 
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(2) rewrite goals using user supplied definitions 
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397 
(3) repeatedly resolve goals with user supplied nondefinitions*) 
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398 

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399 
val is_def = Logic.is_equals o #prop o rep_thm; 
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400 

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401 
fun axclass_tac thms = 
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402 
let 
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403 
val defs = List.filter is_def thms; 
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404 
val non_defs = filter_out is_def thms; 
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405 
in 
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406 
intro_classes_tac [] THEN 
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407 
TRY (rewrite_goals_tac defs) THEN 
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408 
TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i)) 
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409 
end; 
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410 

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411 

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412 
(* instance declarations *) 
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413 

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414 
local 
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415 

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416 
fun prove mk_prop str_of sign prop thms usr_tac = 
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417 
(Tactic.prove sign [] [] (mk_prop prop) 
15973  418 
(K (axclass_tac thms THEN (if_none usr_tac all_tac))) 
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419 
handle ERROR => error ("The error(s) above occurred while trying to prove " ^ 
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420 
quote (str_of sign prop))) > Drule.standard; 
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421 

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422 
val prove_subclass = prove mk_classrel (fn sg => fn (c1, c2) => 
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423 
Pretty.string_of_classrel (Sign.pp sg) [c1, c2]); 
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424 

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425 
val prove_arity = prove mk_arity (fn sg => fn (t, Ss, c) => 
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426 
Pretty.string_of_arity (Sign.pp sg) (t, Ss, [c])); 
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427 

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428 
fun witnesses thy names thms = 
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429 
PureThy.get_thmss thy (map (rpair NONE) names) @ thms @ List.filter is_def (map snd (axioms_of thy)); 
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430 

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431 
in 
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432 

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433 
fun add_inst_subclass_x raw_c1_c2 names thms usr_tac thy = 
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434 
let 
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435 
val sign = Theory.sign_of thy; 
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436 
val (c1, c2) = read_classrel sign raw_c1_c2; 
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437 
in 
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438 
message ("Proving class inclusion " ^ quote (Sign.string_of_classrel sign [c1, c2]) ^ " ..."); 
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439 
thy > add_classrel_thms [prove_subclass sign (c1, c2) (witnesses thy names thms) usr_tac] 
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440 
end; 
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441 

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442 
fun add_inst_arity_x raw_arity names thms usr_tac thy = 
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443 
let 
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444 
val sign = Theory.sign_of thy; 
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445 
val (t, Ss, cs) = read_arity sign raw_arity; 
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446 
val wthms = witnesses thy names thms; 
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447 
fun prove c = 
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448 
(message ("Proving type arity " ^ 
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449 
quote (Sign.string_of_arity sign (t, Ss, [c])) ^ " ..."); 
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450 
prove_arity sign (t, Ss, c) wthms usr_tac); 
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451 
in add_arity_thms (map prove cs) thy end; 
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452 

404
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453 
end; 
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454 

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455 
end; 