src/Pure/axclass.ML
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Tue, 04 Oct 2005 19:01:37 +0200
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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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  (*legacy interfaces*)
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  val axclass_tac: thm list -> tactic
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  val add_inst_subclass_x: xstring * xstring -> 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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(** 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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(* 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 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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(* get and put data *)
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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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(* class_axms *)
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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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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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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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fun read_class thy c = Sign.certify_class thy (Sign.intern_class thy c);
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fun test_classrel thy cc = (Type.add_classrel (Sign.pp thy) [cc] (Sign.tsig_of thy); cc);
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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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fun test_arity thy ar = (Type.add_arities (Sign.pp thy) [ar] (Sign.tsig_of thy); ar);
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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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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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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 = Tactic.prove thy [] [] (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 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 = Tactic.prove_multi thy [] [] 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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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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(* instance declarations -- Isar proof *)
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local
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fun gen_instance mk_prop add_thms inst thy = thy
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  |> ProofContext.init
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  |> Proof.theorem_i Drule.internalK (K (fold add_thms)) NONE ("", [])
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    (map (fn t => (("", []), [(t, ([], []))])) (mk_prop thy inst));
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in
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val instance_subclass =
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  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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end;
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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.theory_of_thm st))))
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    THEN Tactic.distinct_subgoals_tac) st;
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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!*)
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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;
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val _ = Context.add_setup [Method.add_methods
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 [("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
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   "back-chain introduction rules of axiomatic type classes"),
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  ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule")]];
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(** outer syntax **)
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local structure P = OuterParse and K = OuterKeyword in
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val axclassP =
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  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 (#1 oo uncurry add_axclass)));
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val instanceP =
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  OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal
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   ((P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.!!! P.xname) >> instance_subclass ||
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      P.xname -- (P.$$$ "::" |-- P.!!! P.arity) >> (instance_arity o P.triple2))
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    >> (Toplevel.print oo Toplevel.theory_to_proof));
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val _ = OuterSyntax.add_parsers [axclassP, instanceP];
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end;
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(** old-style instantiation proofs **)
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(* axclass_tac *)
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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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  (3) repeatedly resolve goals with user supplied non-definitions*)
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val is_def = Logic.is_equals o #prop o rep_thm;
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fun axclass_tac thms =
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  let
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    val defs = List.filter is_def thms;
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    val non_defs = filter_out is_def thms;
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  in
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    intro_classes_tac [] THEN
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    TRY (rewrite_goals_tac defs) THEN
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    TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
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  end;
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(* instance declarations *)
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local
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fun prove mk_prop str_of thy prop thms usr_tac =
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  (Tactic.prove thy [] [] (mk_prop prop)
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      (K (axclass_tac thms THEN (if_none usr_tac all_tac)))
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    handle ERROR => error ("The error(s) above occurred while trying to prove " ^
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     quote (str_of thy prop))) |> Drule.standard;
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val prove_subclass = prove mk_classrel (fn thy => fn (c1, c2) =>
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  Pretty.string_of_classrel (Sign.pp thy) [c1, c2]);
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val prove_arity = prove mk_arity (fn thy => fn (t, Ss, c) =>
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  Pretty.string_of_arity (Sign.pp thy) (t, Ss, [c]));
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fun witnesses thy names thms =
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  PureThy.get_thmss thy (map Name names) @
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  thms @
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  List.filter is_def (map snd (axioms_of thy));
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in
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fun add_inst_subclass_x raw_c1_c2 names thms usr_tac thy =
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  let val (c1, c2) = read_classrel thy raw_c1_c2 in
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    message ("Proving class inclusion " ^ quote (Sign.string_of_classrel thy [c1, c2]) ^ " ...");
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    thy |> add_classrel_thms [prove_subclass thy (c1, c2) (witnesses thy names thms) usr_tac]
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  end;
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fun add_inst_arity_x raw_arity names thms usr_tac thy =
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  let
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    val (t, Ss, cs) = read_arity thy raw_arity;
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    val wthms = witnesses thy names thms;
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    fun prove c =
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     (message ("Proving type arity " ^
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        quote (Sign.string_of_arity thy (t, Ss, [c])) ^ " ...");
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        prove_arity thy (t, Ss, c) wthms usr_tac);
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  in add_arity_thms (map prove cs) thy end;
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end;
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end;