src/Pure/axclass.ML
author wenzelm
Mon, 24 May 1999 21:53:18 +0200
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outer syntax keyword classification; no open OuterParse;
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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 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_axclass: bclass * xclass list -> ((bstring * string) * Args.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_inst_subclass: xclass * xclass -> string list -> thm list
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    -> tactic option -> theory -> theory
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  val add_inst_subclass_i: class * class -> string list -> thm list
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    -> tactic option -> theory -> theory
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  val add_inst_arity: xstring * xsort list * xclass list -> string list
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    -> thm list -> tactic option -> theory -> theory
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  val add_inst_arity_i: string * sort list * class list -> string list
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    -> thm list -> tactic option -> theory -> theory
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  val axclass_tac: thm list -> tactic
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  val prove_subclass: theory -> class * class -> thm list
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    -> tactic option -> thm
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  val prove_arity: theory -> string * sort list * class -> thm list
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    -> tactic option -> thm
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  val goal_subclass: theory -> xclass * xclass -> thm list
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  val goal_arity: theory -> xstring * xsort list * xclass -> thm list
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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 * xsort list * xclass -> bool -> theory -> ProofHistory.T
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  val instance_arity_proof_i: string * sort list * class -> bool -> theory -> ProofHistory.T
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  val setup: (theory -> theory) list
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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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(* get axioms and theorems *)
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val is_def = Logic.is_equals o #prop o rep_thm;
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fun witnesses thy names thms =
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  PureThy.get_thmss thy names @ thms @ filter is_def (map snd (axioms_of thy));
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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 names = tl (variantlist (replicate (length ss + 1) "'", []));
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    val tfrees = ListPair.map TFree (names, ss);
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  in Logic.mk_inclass (Type (t, tfrees), c) end;
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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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(** add theorems as axioms **)
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fun prep_thm_axm thy thm =
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  let
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    fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
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    val {sign, hyps, prop, ...} = rep_thm thm;
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  in
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    if not (Sign.subsig (sign, Theory.sign_of thy)) then
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      err "theorem not of same theory"
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    else if not (null (extra_shyps thm)) orelse not (null hyps) then
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      err "theorem may not contain hypotheses"
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    else prop
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  end;
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(*theorems expressing class relations*)
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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 = prep_thm_axm thy thm;
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        val (c1, c2) = dest_classrel prop handle TERM _ =>
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          raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
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      in (c1, c2) end;
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  in Theory.add_classrel (map prep_thm thms) thy end;
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(*theorems expressing arities*)
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fun add_arity_thms thms thy =
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  let
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    fun prep_thm thm =
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      let
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        val prop = prep_thm_axm thy thm;
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        val (t, ss, c) = dest_arity prop handle TERM _ =>
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          raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
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      in (t, ss, [c]) end;
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  in Theory.add_arities (map prep_thm thms) thy 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.cond_extern sg Sign.classK;
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      val ext_thm = PureThy.cond_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 ^ ":") (map Display.pretty_thm 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 seq (Pretty.writeln o pretty_axclass) (Symtab.dest tab) end;
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end;
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structure AxclassesData = TheoryDataFun(AxclassesArgs);
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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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(** add axiomatic type classes **)
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(* errors *)
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fun err_not_logic c =
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  error ("Axiomatic class " ^ quote c ^ " not subclass of " ^ quote logicC);
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fun err_bad_axsort ax c =
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  error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
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fun err_bad_tfrees ax =
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  error ("More than one type variable in axiom " ^ quote ax);
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(* ext_axclass *)
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fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy =
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  let
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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 logicS, 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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    (*prepare introduction rule*)
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    val _ = if Sign.subsort class_sign ([class], logicS) then () else err_not_logic class;
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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.norm_sort class_sign (logicC :: flat (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 =
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      class_thy
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      |> Theory.add_path 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 intro = PureThy.get_thm axms_thy introN;
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    val axioms = PureThy.get_thms axms_thy axiomsN;
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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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      |> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)
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      |> Theory.parent_path
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      |> 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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(* external interfaces *)
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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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(** prove class relations and type arities **)
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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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    mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes
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  end;
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(* expand classes *)
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fun expand_classes_tac st =
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  TRY (REPEAT_FIRST (resolve_tac (class_axms (Thm.sign_of_thm st)))) st;
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val expand_classes_method =
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  ("expand_classes", Method.no_args (Method.METHOD0 expand_classes_tac),
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    "expand axiomatic type classes");
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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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fun axclass_tac thms =
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  let
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    val defs = 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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    expand_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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(* provers *)
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fun prove mk_prop str_of thy sig_prop thms usr_tac =
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  let
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    val sign = Theory.sign_of thy;
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    val goal = Thm.cterm_of sign (mk_prop sig_prop)
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      handle TERM (msg, _) => error msg
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        | TYPE (msg, _, _) => error msg;
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    val tac = axclass_tac thms THEN (if_none usr_tac all_tac);
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  in
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    prove_goalw_cterm [] goal (K [tac])
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  end
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  handle ERROR => error ("The error(s) above occurred while trying to prove "
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    ^ quote (str_of (Theory.sign_of thy, sig_prop)));
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val prove_subclass =
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  prove mk_classrel (fn (sg, c1_c2) => Sign.str_of_classrel sg c1_c2);
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val prove_arity =
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  prove mk_arity (fn (sg, (t, Ss, c)) => Sign.str_of_arity sg (t, Ss, [c]));
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(** add proved subclass relations and arities **)
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fun intrn_classrel sg c1_c2 =
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  pairself (Sign.intern_class sg) c1_c2;
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fun intrn_arity intrn sg (t, Ss, x) =
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  (Sign.intern_tycon sg t, map (Sign.intern_sort sg) Ss, intrn sg x);
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fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy =
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  let val c1_c2 = prep_classrel (Theory.sign_of thy) raw_c1_c2 in
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    message ("Proving class inclusion " ^
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      quote (Sign.str_of_classrel (Theory.sign_of 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 ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy =
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  let
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    val sign = Theory.sign_of thy;
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    val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs);
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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.str_of_arity sign (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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val add_inst_subclass = ext_inst_subclass intrn_classrel;
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val add_inst_subclass_i = ext_inst_subclass (K I);
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val add_inst_arity = ext_inst_arity (intrn_arity Sign.intern_sort);
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val add_inst_arity_i = ext_inst_arity (K I);
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(* make old-style interactive goals *)
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fun mk_goal mk_prop thy sig_prop =
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  Goals.goalw_cterm [] (Thm.cterm_of (Theory.sign_of thy) (mk_prop (Theory.sign_of thy) sig_prop));
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val goal_subclass = mk_goal (mk_classrel oo intrn_classrel);
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val goal_arity = mk_goal (mk_arity oo intrn_arity Sign.intern_class);
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(** instance proof interfaces **)
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fun inst_attribute add_thms (thy, thm) = (add_thms [thm] thy, thm);
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6679
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fun inst_proof mk_prop add_thms sig_prop int thy =
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  thy
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  |> IsarThy.theorem_i "" [inst_attribute add_thms]
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    (mk_prop (Theory.sign_of thy) sig_prop, []) int;
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val instance_subclass_proof = inst_proof (mk_classrel oo intrn_classrel) add_classrel_thms;
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val instance_subclass_proof_i = inst_proof (K mk_classrel) add_classrel_thms;
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val instance_arity_proof = inst_proof (mk_arity oo intrn_arity Sign.intern_class) add_arity_thms;
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val instance_arity_proof_i = inst_proof (K mk_arity) add_arity_thms;
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(** package setup **)
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(* setup theory *)
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val setup =
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 [AxclassesData.init,
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  Method.add_methods [expand_classes_method]];
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(* outer syntax *)
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local structure P = OuterParse and K = OuterSyntax.Keyword 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.$$$ "<" |-- P.!!! (P.list1 P.xname)) [] -- Scan.repeat P.spec_name
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      >> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs)));
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val instanceP =
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  OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal
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    ((P.xname -- (P.$$$ "<" |-- P.xname) >> instance_subclass_proof ||
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   439
      P.xname -- (P.$$$ "::" |-- P.simple_arity) >> (instance_arity_proof 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;
3949
c60ff6d0a6b8 fixed goal_XXX;
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c60ff6d0a6b8 fixed goal_XXX;
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404
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end;