author  wenzelm 
Sat, 14 Jan 2006 17:14:06 +0100  
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parent 18574  46ed84a64cf6 
child 18708  4b3dadb4fe33 
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 
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val get_info: theory > string > {super_classes: class list, intro: thm, axioms: thm list} 
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val add_axclass: bstring * xstring list > ((bstring * string) * Attrib.src list) list > 
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theory > {intro: thm, axioms: thm list} * theory 
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val add_axclass_i: bstring * class list > ((bstring * term) * theory attribute list) list > 
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theory > {intro: thm, axioms: thm list} * theory 
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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: xstring * xstring > 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: xstring * xstring > theory > Proof.state 
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val instance_subclass_i: class * class > theory > Proof.state 

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val instance_arity: xstring * string list * string > theory > Proof.state 

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val instance_arity_i: string * sort list * sort > theory > Proof.state 

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val read_arity: theory > xstring * string list * string > arity 
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val cert_arity: theory > string * sort list * sort > arity 

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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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end; 
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15801  33 
structure AxClass: AX_CLASS = 
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struct 
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4015  36 

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(** utilities **) 
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5685  39 
(* messages *) 
40 

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val quiet_mode = ref false; 

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

43 

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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 

3788  57 
 dest_varT T = raise TYPE ("dest_varT", [T], []); 
3395  58 

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(** abstract syntax operations **) 
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(* names *) 
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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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1498  71 
fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2); 
423  72 

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fun dest_classrel tm = 

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let 

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fun err () = raise TERM ("dest_classrel", [tm]); 
423  76 

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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; 
423  81 

82 

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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 (op =)) tvars) 
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then map snd tvars else err (); 
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in (t, ss, c) end; 
423  105 

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6379  108 
(** axclass info **) 
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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 AxclassesData = TheoryDataFun 
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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 extend = I; 
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fun merge _ = Symtab.merge (K true); 

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fun print thy tab = 
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let 
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fun pretty_class c cs = Pretty.block 

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(Pretty.str (Sign.extern_class thy c) :: Pretty.str " <" :: Pretty.brk 1 :: 
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Pretty.breaks (map (Pretty.str o Sign.extern_class thy) cs)); 

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fun pretty_thms name thms = Pretty.big_list (name ^ ":") 
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(map (Display.pretty_thm_sg thy) 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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val _ = Context.add_setup [AxclassesData.init]; 
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val print_axclasses = AxclassesData.print; 
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val lookup_info = Symtab.lookup o AxclassesData.get; 
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fun get_info thy c = 
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(case lookup_info 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 class_axms thy = 
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let val classes = Sign.classes thy in 

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map (Thm.class_triv thy) classes @ 

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List.mapPartial (Option.map #intro o lookup_info thy) classes 
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end; 
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423  158 

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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 class = Sign.full_name thy bclass; 
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val super_classes = map (prep_class thy) raw_super_classes; 

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val axms = map (prep_axm thy 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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(*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 snd) 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_thy ([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_thy (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*) 

18377  201 
val (([intro], [axioms]), axms_thy) = 
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class_thy 
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> Theory.add_path (Sign.const_of_class bclass) 
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> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)] 
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>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; 
6379  206 
val info = {super_classes = super_classes, intro = intro, axioms = axioms}; 
207 

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(*store info*) 

18377  209 
val (_, final_thy) = 
6379  210 
axms_thy 
17703  211 
> Theory.add_finals_i false [Const (Sign.const_of_class class, a_itselfT > propT)] 
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> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts) 
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> Theory.restore_naming class_thy 

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> AxclassesData.map (Symtab.update (class, info)); 

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in ({intro = intro, axioms = axioms}, final_thy) 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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(* prepare classes and arities *) 
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16458  253 
fun read_class thy c = Sign.certify_class thy (Sign.intern_class thy c); 
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16458  255 
fun test_classrel thy cc = (Type.add_classrel (Sign.pp thy) [cc] (Sign.tsig_of thy); cc); 
256 
fun cert_classrel thy = test_classrel thy o Library.pairself (Sign.certify_class thy); 

257 
fun read_classrel thy = test_classrel thy o Library.pairself (read_class thy); 

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16458  259 
fun test_arity thy ar = (Type.add_arities (Sign.pp thy) [ar] (Sign.tsig_of thy); ar); 
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16458  261 
fun prep_arity prep_tycon prep_sort prep thy (t, Ss, x) = 
262 
test_arity thy (prep_tycon thy t, map (prep_sort thy) Ss, prep thy x); 

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16364  264 
val read_arity = prep_arity Sign.intern_type 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  271 

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fun ext_inst_subclass prep_classrel raw_cc tac thy = 
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let 
16458  274 
val (c1, c2) = prep_classrel thy raw_cc; 
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val txt = quote (Sign.string_of_classrel thy [c1, c2]); 

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val _ = message ("Proving class inclusion " ^ txt ^ " ..."); 
18678  277 
val th = Goal.prove thy [] [] (mk_classrel (c1, c2)) (K tac) handle ERROR msg => 
278 
cat_error msg ("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 
16458  283 
val arity = prep_arity thy raw_arity; 
284 
val txt = quote (Sign.string_of_arity thy arity); 

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val _ = message ("Proving type arity " ^ txt ^ " ..."); 
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val props = (mk_arities arity); 
17956  287 
val ths = Goal.prove_multi thy [] [] props 
18678  288 
(fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg => 
289 
cat_error msg ("\nThe error(s) above occurred while trying to prove " ^ txt); 

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in add_arity_thms ths thy end; 
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in 
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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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end; 
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423  301 

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(* instance declarations  Isar proof *) 
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local 
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17339  306 
fun gen_instance mk_prop add_thms inst thy = thy 
307 
> ProofContext.init 

18124  308 
> Proof.theorem_i Drule.internalK NONE (fold add_thms) NONE ("", []) 
17339  309 
(map (fn t => (("", []), [(t, ([], []))])) (mk_prop thy inst)); 
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in 
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17339  313 
val instance_subclass = 
314 
gen_instance (single oo (mk_classrel oo read_classrel)) add_classrel_thms; 

315 
val instance_subclass_i = 

316 
gen_instance (single oo (mk_classrel oo cert_classrel)) add_classrel_thms; 

317 
val instance_arity = gen_instance (mk_arities oo read_arity) add_arity_thms; 

318 
val instance_arity_i = gen_instance (mk_arities oo cert_arity) add_arity_thms; 

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end; 
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(* tactics and methods *) 
6379  324 

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fun intro_classes_tac facts st = 
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(ALLGOALS (Method.insert_tac facts THEN' 
16458  327 
REPEAT_ALL_NEW (resolve_tac (class_axms (Thm.theory_of_thm st)))) 
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THEN Tactic.distinct_subgoals_tac) st; 
6379  329 

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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  332 

333 
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  336 

15801  337 
val _ = Context.add_setup [Method.add_methods 
338 
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac), 

339 
"backchain introduction rules of axiomatic type classes"), 

340 
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule")]]; 

10309  341 

342 

423  343 

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(** outer syntax **) 
6379  345 

17057  346 
local structure P = OuterParse and K = OuterKeyword in 
3949  347 

6379  348 
val axclassP = 
6719  349 
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 
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>> (Toplevel.theory o (snd oo uncurry add_axclass))); 
6379  353 

354 
val instanceP = 

6719  355 
OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal 
17339  356 
((P.xname  ((P.$$$ "\\<subseteq>"  P.$$$ "<")  P.!!! P.xname) >> instance_subclass  
357 
P.xname  (P.$$$ "::"  P.!!! P.arity) >> (instance_arity o P.triple2)) 

358 
>> (Toplevel.print oo Toplevel.theory_to_proof)); 

6379  359 

360 
val _ = OuterSyntax.add_parsers [axclassP, instanceP]; 

361 

362 
end; 

3949  363 

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end; 