author | wenzelm |
Tue, 08 Nov 2005 10:44:40 +0100 | |
changeset 18124 | a310c78298f9 |
parent 17956 | 369e2af8ee45 |
child 18377 | 0e1d025d57b3 |
permissions | -rw-r--r-- |
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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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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 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 -> theory * {intro: thm, axioms: thm list} |
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val add_axclass_i: bstring * 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: 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 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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structure AxClass: AX_CLASS = |
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struct |
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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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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 (op =)) 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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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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(** 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*) |
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val (axms_thy, ([intro], [axioms])) = |
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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)]; |
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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 |
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|> Theory.add_finals_i false [Const (Sign.const_of_class class, a_itselfT --> propT)] |
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|> (#1 o 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 (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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|
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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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|
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|
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(* prepare classes and arities *) |
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|
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fun read_class thy c = Sign.certify_class thy (Sign.intern_class thy c); |
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|
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fun test_classrel thy cc = (Type.add_classrel (Sign.pp thy) [cc] (Sign.tsig_of thy); cc); |
254 |
fun cert_classrel thy = test_classrel thy o Library.pairself (Sign.certify_class thy); |
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fun read_classrel thy = test_classrel thy o Library.pairself (read_class thy); |
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|
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fun test_arity thy ar = (Type.add_arities (Sign.pp thy) [ar] (Sign.tsig_of thy); ar); |
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|
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fun prep_arity prep_tycon prep_sort prep thy (t, Ss, x) = |
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test_arity thy (prep_tycon thy t, map (prep_sort thy) Ss, prep thy x); |
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|
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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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|
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|
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(* instance declarations -- tactical proof *) |
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|
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local |
423 | 269 |
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fun ext_inst_subclass prep_classrel raw_cc tac thy = |
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let |
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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 ^ " ..."); |
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val th = Goal.prove thy [] [] (mk_classrel (c1, c2)) (K tac) handle ERROR_MESSAGE msg => |
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error (msg ^ "\nThe error(s) above occurred while trying to prove " ^ txt); |
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in add_classrel_thms [th] thy end; |
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|
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fun ext_inst_arity prep_arity raw_arity tac thy = |
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let |
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val arity = prep_arity thy raw_arity; |
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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); |
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val ths = Goal.prove_multi thy [] [] props |
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(fn _ => Tactic.smart_conjunction_tac (length props) THEN tac) handle ERROR_MESSAGE msg => |
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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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|
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in |
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|
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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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|
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end; |
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|
423 | 299 |
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(* instance declarations -- Isar proof *) |
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|
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local |
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|
17339 | 304 |
fun gen_instance mk_prop add_thms inst thy = thy |
305 |
|> ProofContext.init |
|
18124 | 306 |
|> Proof.theorem_i Drule.internalK NONE (fold add_thms) NONE ("", []) |
17339 | 307 |
(map (fn t => (("", []), [(t, ([], []))])) (mk_prop thy inst)); |
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|
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in |
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|
17339 | 311 |
val instance_subclass = |
312 |
gen_instance (single oo (mk_classrel oo read_classrel)) add_classrel_thms; |
|
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val instance_subclass_i = |
|
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gen_instance (single oo (mk_classrel oo cert_classrel)) add_classrel_thms; |
|
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val instance_arity = gen_instance (mk_arities oo read_arity) add_arity_thms; |
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val instance_arity_i = gen_instance (mk_arities oo cert_arity) add_arity_thms; |
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|
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end; |
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|
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(* tactics and methods *) |
6379 | 322 |
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fun intro_classes_tac facts st = |
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(ALLGOALS (Method.insert_tac facts THEN' |
16458 | 325 |
REPEAT_ALL_NEW (resolve_tac (class_axms (Thm.theory_of_thm st)))) |
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THEN Tactic.distinct_subgoals_tac) st; |
6379 | 327 |
|
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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 | 330 |
|
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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 | 334 |
|
15801 | 335 |
val _ = Context.add_setup [Method.add_methods |
336 |
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac), |
|
337 |
"back-chain introduction rules of axiomatic type classes"), |
|
338 |
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule")]]; |
|
10309 | 339 |
|
340 |
||
423 | 341 |
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(** outer syntax **) |
6379 | 343 |
|
17057 | 344 |
local structure P = OuterParse and K = OuterKeyword in |
3949 | 345 |
|
6379 | 346 |
val axclassP = |
6719 | 347 |
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 |
17339 | 350 |
>> (Toplevel.theory o (#1 oo uncurry add_axclass))); |
6379 | 351 |
|
352 |
val instanceP = |
|
6719 | 353 |
OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal |
17339 | 354 |
((P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.!!! P.xname) >> instance_subclass || |
355 |
P.xname -- (P.$$$ "::" |-- P.!!! P.arity) >> (instance_arity o P.triple2)) |
|
356 |
>> (Toplevel.print oo Toplevel.theory_to_proof)); |
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6379 | 357 |
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val _ = OuterSyntax.add_parsers [axclassP, instanceP]; |
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359 |
||
360 |
end; |
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3949 | 361 |
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362 |
end; |