src/Pure/Tools/class_package.ML

tactic for prove_instance_arity now gets definition theorems as arguments

(*  Title:      Pure/Tools/class_package.ML
    ID:         $Id$
    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales.
*)

signature CLASS_PACKAGE =
sig
  val class: bstring -> class list -> Element.context list -> theory
    -> ProofContext.context * theory
  val class_i: bstring -> class list -> Element.context_i list -> theory
    -> ProofContext.context * theory
  (*FIXME: in _i variants, bstring should be bstring option*)
  val instance_arity: ((xstring * string list) * string) list
    -> bstring * Attrib.src list -> ((bstring * Attrib.src list) * string) list
    -> theory -> Proof.state
  val instance_arity_i: ((string * sort list) * sort) list
    -> bstring * attribute list -> ((bstring * attribute list) * term) list
    -> theory -> Proof.state
  val prove_instance_arity: (thm list -> tactic) -> ((string * sort list) * sort) list
    -> bstring * attribute list -> ((bstring * attribute list) * term) list
    -> theory -> theory
  val instance_sort: string * string -> theory -> Proof.state
  val instance_sort_i: class * sort -> theory -> Proof.state
  val prove_instance_sort: tactic -> class * sort -> theory -> theory

  val intern_class: theory -> xstring -> class
  val intern_sort: theory -> sort -> sort
  val extern_class: theory -> class -> xstring
  val extern_sort: theory -> sort -> sort
  val certify_class: theory -> class -> class
  val certify_sort: theory -> sort -> sort
  val read_sort: theory -> string -> sort
  val operational_sort_of: theory -> sort -> sort
  val the_superclasses: theory -> class -> class list
  val the_consts_sign: theory -> class -> string * (string * typ) list
  val the_inst_sign: theory -> class * string -> (string * sort) list * (string * typ) list
  val assume_arities_of_sort: theory -> ((string * sort list) * sort) list -> typ * sort -> bool
  val assume_arities_thy: theory -> ((string * sort list) * sort) list -> (theory -> 'a) -> 'a
    (*'a must not keep any reference to theory*)

  val print_classes: theory -> unit
  val intro_classes_tac: thm list -> tactic
  val default_intro_classes_tac: thm list -> tactic

  type sortcontext = (string * sort) list
  datatype classlookup = Instance of (class * string) * classlookup list list
                       | Lookup of class list * (string * (int * int))
  val sortcontext_of_typ: theory -> typ -> sortcontext
  val sortlookup: theory -> sort * typ -> classlookup list
  val sortlookups_const: theory -> string * typ -> classlookup list list
end;

structure ClassPackage : CLASS_PACKAGE =
struct


(* auxiliary *)

fun instantiations_of thy (ty, ty') =
  let
    val vartab = typ_tvars ty;
    fun prep_vartab (v, (_, ty)) =
      case (the o AList.lookup (op =) vartab) v
       of [] => NONE
        | sort => SOME ((v, sort), ty);
  in case try (Sign.typ_match thy (ty, ty')) Vartab.empty
   of NONE => NONE
    | SOME vartab =>
        SOME ((map_filter prep_vartab o Vartab.dest) vartab)
  end;


(* theory data *)

datatype class_data = ClassData of {
  name_locale: string,
  name_axclass: string,
  var: string,
  consts: (string * (string * typ)) list,
    (*locale parameter ~> toplevel constant*)
  propnames: string list
} * thm list Symtab.table;

fun rep_classdata (ClassData c) = c;

structure ClassData = TheoryDataFun (
  struct
    val name = "Pure/classes";
    type T = class_data Symtab.table;
    val empty = Symtab.empty;
    val copy = I;
    val extend = I;
    fun merge _ = Symtab.join (fn _ => fn (ClassData (classd, instd1), ClassData (_, instd2)) =>
      (ClassData (classd, Symtab.merge (K true) (instd1, instd2))));
    fun print thy data =
      let
        fun pretty_class (name, ClassData ({name_locale, name_axclass, var, consts, ...}, _)) =
          (Pretty.block o Pretty.fbreaks) [
            Pretty.str ("class " ^ name ^ ":"),
            Pretty.str ("locale: " ^ name_locale),
            Pretty.str ("axclass: " ^ name_axclass),
            Pretty.str ("class variable: " ^ var),
            (Pretty.block o Pretty.fbreaks) (
              Pretty.str "constants: "
              :: map (fn (_, (c, ty)) => Pretty.str (c ^ " :: " ^ Sign.string_of_typ thy ty)) consts
            )
          ]
      in
        (Pretty.writeln o Pretty.chunks o map pretty_class o Symtab.dest) data
      end;
  end
);

val _ = Context.add_setup ClassData.init;
val print_classes = ClassData.print;


(* queries *)

val lookup_class_data = Option.map rep_classdata oo Symtab.lookup o ClassData.get;

fun the_class_data thy class =
  case lookup_class_data thy class
    of NONE => error ("undeclared operational class " ^ quote class)
     | SOME data => data;

val is_class = is_some oo lookup_class_data;

fun is_operational_class thy cls =
  lookup_class_data thy cls
  |> Option.map (not o null o #consts o fst)
  |> the_default false;

fun operational_sort_of thy =
  let
    fun get_sort class =
      if is_operational_class thy class
      then [class]
      else operational_sort_of thy (Sign.super_classes thy class);
  in Sign.certify_sort thy o maps get_sort end;

fun the_superclasses thy class =
  if is_class thy class
  then
    Sign.super_classes thy class
    |> operational_sort_of thy
  else
    error ("no operational class: " ^ class);

fun the_ancestry thy classes =
  let
    fun ancestry class anc =
      anc
      |> cons class
      |> fold ancestry (the_superclasses thy class);
  in fold ancestry classes [] end;

fun subst_clsvar v ty_subst =
  map_type_tfree (fn u as (w, _) =>
    if w = v then ty_subst else TFree u);

val the_parm_map = #consts o fst oo the_class_data;

fun the_consts_sign thy class =
  let
    val data = (fst o the_class_data thy) class
  in (#var data, (map snd o #consts) data) end;

fun the_inst_sign thy (class, tyco) =
  let
    val _ = if is_operational_class thy class then () else error ("no operational class: " ^ class);
    val asorts = Sign.arity_sorts thy tyco [class];
    val (clsvar, const_sign) = the_consts_sign thy class;
    fun add_var sort used =
      let val v = hd (Name.invents used "'a" 1);
      in ((v, sort), Name.declare v used) end;
    val (vsorts, _) =
      Name.context
      |> Name.declare clsvar
      |> fold (fn (_, ty) => fold Name.declare
           ((map (fst o fst) o typ_tvars) ty @ (map fst o typ_tfrees) ty)) const_sign
      |> fold_map add_var asorts;
    val ty_inst = Type (tyco, map TFree vsorts);
    val inst_signs = map (apsnd (subst_clsvar clsvar ty_inst)) const_sign;
  in (vsorts, inst_signs) end;

val the_propnames = #propnames o fst oo the_class_data;


(* updaters *)

fun add_class_data (class, (name_locale, name_axclass, var, consts, propnames)) =
  ClassData.map (
    Symtab.update_new (class, ClassData ({
      name_locale = name_locale,
      name_axclass = name_axclass,
      var = var,
      consts = consts,
      propnames = propnames}, Symtab.empty))
  );

fun add_inst_def ((class, tyco), thm) =
  ClassData.map (
    Symtab.map_entry class (fn ClassData (classd, instd) =>
      ClassData (classd, Symtab.insert_list eq_thm (tyco, thm) instd))
  );


(* name handling *)

fun certify_class thy class =
  (fn class => (the_class_data thy class; class)) (Sign.certify_class thy class);

fun certify_sort thy sort =
  map (fn class => (the_class_data thy class; class)) (Sign.certify_sort thy sort);

fun intern_class thy =
  certify_class thy o Sign.intern_class thy;

fun intern_sort thy =
  certify_sort thy o Sign.intern_sort thy;

fun extern_class thy =
  Sign.extern_class thy o certify_class thy;

fun extern_sort thy =
  Sign.extern_sort thy o certify_sort thy;

fun read_sort thy =
  certify_sort thy o Sign.read_sort thy;


(* contexts with arity assumptions *)

fun assume_arities_of_sort thy arities ty_sort =
  let
    val pp = Sign.pp thy;
    val algebra = Sign.classes_of thy
      |> fold (fn ((tyco, asorts), sort) =>
           Sorts.add_arities pp (tyco, map (fn class => (class, asorts)) sort)) arities;
  in Sorts.of_sort algebra ty_sort end;

fun assume_arities_thy thy arities f =
  let
    val thy_read = (fold (fn ((tyco, asorts), sort)
      => Sign.primitive_arity (tyco, asorts, sort)) arities o Theory.copy) thy
  in f thy_read end;

(* tactics and methods *)

fun intro_classes_tac facts st =
  (ALLGOALS (Method.insert_tac facts THEN'
      REPEAT_ALL_NEW (resolve_tac (AxClass.class_intros (Thm.theory_of_thm st))))
    THEN Tactic.distinct_subgoals_tac) st;

fun default_intro_classes_tac [] = intro_classes_tac []
  | default_intro_classes_tac _ = Tactical.no_tac;    (*no error message!*)

fun default_tac rules ctxt facts =
  HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
    default_intro_classes_tac facts;

val _ = Context.add_setup (Method.add_methods
 [("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
    "back-chain introduction rules of classes"),
  ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),
    "apply some intro/elim rule")]);


(* axclass instances *)

local

fun gen_instance mk_prop add_thm after_qed insts thy =
  thy
  |> ProofContext.init
  |> Proof.theorem_i PureThy.internalK NONE (after_qed oo (fold o fold) add_thm) NONE ("", [])
       ((map (fn t => (("", []), [(t, [])])) o maps (mk_prop thy)) insts);

in

val axclass_instance_arity =
  gen_instance (Logic.mk_arities oo Sign.read_arity) AxClass.add_arity;
val axclass_instance_arity_i =
  gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
val axclass_instance_sort =      
  gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel)) AxClass.add_classrel I o single;

end;


(* classes and instances *)

local

fun add_axclass_i (name, supsort) params axs thy =
  let
    val (c, thy') = thy
      |> AxClass.define_class_i (name, supsort) params axs;
    val {intro, axioms, ...} = AxClass.get_definition thy' c;
  in ((c, (intro, axioms)), thy') end;

fun prove_interpretation_i (prfx, atts) expr insts tac thy =
  let
    fun ad_hoc_term NONE = NONE
      | ad_hoc_term (SOME (Const (c, ty))) =
          let
            val p = setmp show_types true (setmp show_sorts true (setmp print_mode [] (Sign.pretty_typ thy))) ty;
            val s = c ^ "::" ^ Pretty.output p;
          in SOME s end
      | ad_hoc_term (SOME t) =
          let
            val p = setmp show_types true (setmp show_sorts true (setmp print_mode [] (Sign.pretty_term thy))) t;
            val s = Pretty.output p;
          in SOME s end;
  in
    thy
    |> Locale.interpretation (prfx, atts) expr (map ad_hoc_term insts)
    |> Proof.global_terminal_proof (Method.Basic (fn _ => Method.SIMPLE_METHOD tac), NONE)
    |-> (fn _ => I)
  end;

fun gen_class add_locale prep_class bname raw_supclasses raw_elems thy =
  let
    val supclasses = map (prep_class thy) raw_supclasses;
    val supsort =
      supclasses
      |> map (#name_axclass o fst o the_class_data thy)
      |> Sign.certify_sort thy
      |> null ? K (Sign.defaultS thy);
    val expr = (Locale.Merge o map (Locale.Locale o #name_locale o fst o the_class_data thy)) supclasses;
    val mapp_sup = AList.make
      (the o AList.lookup (op =) ((flat o map (the_parm_map thy) o the_ancestry thy) supclasses))
      ((map (fst o fst) o Locale.parameters_of_expr thy) expr);
    fun extract_tyvar_consts thy name_locale =
      let
        fun extract_classvar ((c, ty), _) w =
          (case add_typ_tfrees (ty, [])
           of [(v, _)] => (case w
               of SOME u => if u = v then w else error ("additonal type variable in type signature of constant " ^ quote c)
                | NONE => SOME v)
            | [] => error ("no type variable in type signature of constant " ^ quote c)
            | _ => error ("more than one type variable in type signature of constant " ^ quote c));
        val consts1 =
          Locale.parameters_of thy name_locale
          |> map (apsnd Syntax.unlocalize_mixfix)
        val SOME v = fold extract_classvar consts1 NONE;
        val consts2 = map ((apfst o apsnd) (subst_clsvar v (TFree (v, [])))) consts1;
      in (v, chop (length mapp_sup) consts2) end;
    fun add_consts v raw_cs_sup raw_cs_this thy =
      let
        fun add_global_const ((c, ty), syn) thy =
          thy
          |> Sign.add_consts_i [(c, ty |> subst_clsvar v (TFree (v, Sign.defaultS thy)), syn)]
          |> `(fn thy => (c, (Sign.intern_const thy c, ty)))
      in
        thy
        |> fold_map add_global_const raw_cs_this
      end;
    fun extract_assumes thy name_locale cs_mapp =
      let
        val subst_assume =
          map_aterms (fn Free (c, ty) => Const ((fst o the o AList.lookup (op =) cs_mapp) c, ty)
                       | t => t)
        fun prep_asm ((name, atts), ts) =
          ((NameSpace.base name, map (Attrib.attribute thy) atts), map subst_assume ts)
      in
        (map prep_asm o Locale.local_asms_of thy) name_locale
      end;
    fun add_global_constraint v class (_, (c, ty)) thy =
      thy
      |> Sign.add_const_constraint_i (c, SOME (subst_clsvar v (TFree (v, [class])) ty));
    fun mk_const thy class v (c, ty) =
      Const (c, subst_clsvar v (TFree (v, [class])) ty);
  in
    thy
    |> add_locale bname expr raw_elems
    |-> (fn (name_locale, ctxt) =>
          `(fn thy => extract_tyvar_consts thy name_locale)
    #-> (fn (v, (raw_cs_sup, raw_cs_this)) =>
          add_consts v raw_cs_sup raw_cs_this
    #-> (fn mapp_this =>
          `(fn thy => extract_assumes thy name_locale (mapp_sup @ mapp_this))
    #-> (fn loc_axioms =>
          add_axclass_i (bname, supsort) (map (fst o snd) mapp_this) loc_axioms
    #-> (fn (name_axclass, (_, ax_axioms)) =>
          fold (add_global_constraint v name_axclass) mapp_this
    #> add_class_data (name_locale, (name_locale, name_axclass, v, mapp_this,
         map (fst o fst) loc_axioms))
    #> prove_interpretation_i (NameSpace.base name_locale, [])
          (Locale.Locale name_locale) (map (SOME o mk_const thy name_axclass v) (map snd (mapp_sup @ mapp_this)))
          ((ALLGOALS o ProofContext.fact_tac) ax_axioms)
    #> pair ctxt
    )))))
  end;

in

val class = gen_class (Locale.add_locale false) intern_class;
val class_i = gen_class (Locale.add_locale_i false) certify_class;

end; (* local *)

local

fun gen_read_def thy prep_att read_def ((raw_name, raw_atts), raw_t) =
  let
    val (_, t) = read_def thy (raw_name, raw_t);
    val ((c, ty), _) = Sign.cert_def (Sign.pp thy) t;
    val atts = map (prep_att thy) raw_atts;
    val insts = (Consts.typargs (Sign.consts_of thy) (c, ty))
    fun flat_typ (Type (tyco, tys)) = tyco :: maps flat_typ tys
      | flat_typ _ = [];
    val name = case raw_name
     of "" => let
            val tycos = maps flat_typ insts;
            val names = map NameSpace.base (c :: tycos);
          in Thm.def_name (space_implode "_" names) end
      | _ => raw_name;
  in (c, (insts, ((name, t), atts))) end;

fun read_def thy = gen_read_def thy Attrib.attribute read_axm;
fun read_def_i thy = gen_read_def thy (K I) (K I);

fun gen_instance_arity prep_arity prep_att read_def do_proof raw_arities (raw_name, raw_atts) raw_defs theory =
  let
    fun prep_arity' ((tyco, asorts), sort) = prep_arity theory (tyco, asorts, sort);
    val arities = map prep_arity' raw_arities;
    val arities_pair = map (fn (tyco, asorts, sort) => ((tyco, asorts), sort)) arities;
    val _ = if null arities then error "at least one arity must be given" else ();
    val _ = case (duplicates (op =) o map #1) arities
     of [] => ()
      | dupl_tycos => error ("type constructors occur more than once in arities: "
        ^ (commas o map quote) dupl_tycos);
    val name = case raw_name
     of "" => Thm.def_name ((space_implode "_" o map NameSpace.base)
                (maps (fn (tyco, _, sort) => sort @ [tyco])
                (sort (fn ((tyco1, _, _), (tyco2, _, _)) => string_ord (tyco1, tyco2)) arities)))
      | _ => raw_name;
    val atts = map (prep_att theory) raw_atts;
    fun already_defined (c, ty_inst) = 
      is_some (find_first (fn (_, { lhs = [ty_inst'], ...}) =>
          Sign.typ_instance theory (ty_inst', ty_inst) orelse Sign.typ_instance theory (ty_inst, ty_inst'))
        (Defs.specifications_of (Theory.defs_of theory) c));
    fun get_consts_class tyco ty class =
      let
        val data = (fst o the_class_data theory) class;
        val subst_ty = map_type_tfree (fn (v, sort) =>
          if #var data = v then ty else TVar ((v, 0), sort));
      in
        (map_filter (fn (_, (c, ty)) =>
          if already_defined (c, ty)
          then NONE else SOME ((c, ((tyco, class), subst_ty ty)))) o #consts) data
      end;
    fun get_consts_sort (tyco, asorts, sort) =
      let
        val ty = Type (tyco, map (fn (v, sort) => TVar ((v, 0), sort)) (Name.give_names Name.context "'a" asorts))
      in maps (get_consts_class tyco ty) (the_ancestry theory sort) end;
    val cs = maps get_consts_sort arities;
    fun read_defs defs cs thy_read =
      let
        fun read raw_def cs =
          let
            val (c, (inst, ((_, t), atts))) = read_def thy_read raw_def;
            val ty = Logic.varifyT (Consts.instance (Sign.consts_of thy_read) (c, inst));
            val ((tyco, class), ty') = case AList.lookup (op =) cs c
             of NONE => error ("superfluous definition for constant " ^ quote c)
              | SOME class_ty => class_ty;
            val name = Thm.def_name (NameSpace.base c ^ "_" ^ NameSpace.base tyco);
            val t' = case instantiations_of thy_read (ty, ty')
             of NONE => error ("superfluous definition for constant " ^
                  quote c ^ "::" ^ Sign.string_of_typ thy_read ty)
              | SOME insttab =>
                  map_term_types
                    (Logic.unvarifyT o Term.instantiateT insttab o Logic.varifyT) t
          in (((class, tyco), ((name, t'), atts)), AList.delete (op =) c cs) end;
      in fold_map read defs cs end;
    val (defs, _) = assume_arities_thy theory arities_pair (read_defs raw_defs cs);
    fun get_remove_contraint c thy =
      let
        val ty = Sign.the_const_constraint thy c;
      in
        thy
        |> Sign.add_const_constraint_i (c, NONE)
        |> pair (c, Logic.legacy_unvarifyT ty)
      end;
    fun add_defs defs thy =
      thy
      |> PureThy.add_defs_i true (map snd defs)
      |-> (fn thms => pair (map fst defs ~~ thms));
    fun note_all thy =
      (*FIXME: should avoid binding duplicated names*)
      let
        val thms = maps (fn (tyco, _, sort) => maps (fn class =>
          Symtab.lookup_list
            ((snd o the_class_data thy) class) tyco) (the_ancestry thy sort)) arities;
      in
        thy
        |> PureThy.note_thmss_i PureThy.internalK [((name, atts), [(thms, [])])]
        |> snd
      end;
    fun after_qed cs thy =
      thy
      |> fold Sign.add_const_constraint_i (map (apsnd SOME) cs);
  in
    theory
    |> fold_map get_remove_contraint (map fst cs)
    ||>> add_defs defs
    |-> (fn (cs, def_thms) =>
       fold add_inst_def def_thms
    #> note_all
    #> do_proof (map snd def_thms) (after_qed cs) arities)
  end;

fun instance_arity' do_proof = gen_instance_arity Sign.read_arity Attrib.attribute
  read_def do_proof;
fun instance_arity_i' do_proof = gen_instance_arity Sign.cert_arity (K I)
  read_def_i do_proof;
fun tactic_proof tac def_thms after_qed arities =
  fold (fn arity => AxClass.prove_arity arity (tac def_thms)) arities
  #> after_qed;

in

val instance_arity = instance_arity' (K axclass_instance_arity_i);
val instance_arity_i = instance_arity_i' (K axclass_instance_arity_i);
val prove_instance_arity = instance_arity_i' o tactic_proof;

end; (* local *)

local

fun add_interpretation_in (after_qed : theory -> theory) (name, expr) thy =
  thy
  |> Locale.interpretation_in_locale (name, expr);

fun prove_interpretation_in tac (after_qed : theory -> theory) (name, expr) thy =
  thy
  |> Locale.interpretation_in_locale (name, expr)
  |> Proof.global_terminal_proof (Method.Basic (fn _ => Method.SIMPLE_METHOD tac), NONE)
  |> snd
  |> after_qed;

fun gen_instance_sort prep_class prep_sort do_proof (raw_class, raw_sort) theory =
  let
    val class = prep_class theory raw_class;
    val sort = prep_sort theory raw_sort;
    val loc_name = (#name_locale o fst o the_class_data theory) class;
    val loc_expr =
      (Locale.Merge o map (Locale.Locale o #name_locale o fst o the_class_data theory)) sort;
    val const_names = (map (NameSpace.base o fst o snd)
      o maps (#consts o fst o the_class_data theory)
      o the_ancestry theory) [class];
    fun get_thms thy =
      the_ancestry thy sort
      |> AList.make (the_propnames thy)
      |> map (apsnd (map (NameSpace.append (loc_name))))
      |> map_filter (fn (superclass, thm_names) =>
          case map_filter (try (PureThy.get_thm thy o Name)) thm_names
           of [] => NONE
            | thms => SOME (superclass, thms));
    fun after_qed thy =
      thy
      |> `get_thms
      |-> fold (fn (supclass, thms) => I
            AxClass.prove_classrel (class, supclass)
              (ALLGOALS (K (intro_classes_tac [])) THEN
                (ALLGOALS o ProofContext.fact_tac) thms))
  in
    theory
    |> do_proof after_qed (loc_name, loc_expr)
  end;

fun instance_sort' do_proof = gen_instance_sort intern_class read_sort do_proof;
fun instance_sort_i' do_proof = gen_instance_sort certify_class certify_sort do_proof;
val setup_proof = add_interpretation_in;
val tactic_proof = prove_interpretation_in;

in

val instance_sort = instance_sort' setup_proof;
val instance_sort_i = instance_sort_i' setup_proof;
val prove_instance_sort = instance_sort_i' o tactic_proof;

end; (* local *)


(* extracting dictionary obligations from types *)

type sortcontext = (string * sort) list;

fun sortcontext_of_typ thy ty =
  (typ_tfrees o fst o Type.freeze_thaw_type) ty
  |> map (apsnd (operational_sort_of thy))
  |> filter (not o null o snd);

datatype classlookup = Instance of (class * string) * classlookup list list
                     | Lookup of class list * (string * (int * int))

fun pretty_lookup' (Instance ((class, tyco), lss)) =
      (Pretty.block o Pretty.breaks) (
        Pretty.enum "," "{" "}" [Pretty.str class, Pretty.str tyco]
        :: map pretty_lookup lss
      )
  | pretty_lookup' (Lookup (classes, (v, (i, j)))) =
      Pretty.enum " <" "[" "]" (map Pretty.str classes @
        [Pretty.str (v ^ "!" ^ string_of_int i ^ "/" ^ string_of_int j)])
and pretty_lookup ls = (Pretty.enum "," "(" ")" o map pretty_lookup') ls;

fun sortlookup thy (sort_decl, typ_ctxt) =
  let
    val pp = Sign.pp thy;
    val algebra = Sorts.project_algebra pp (is_operational_class thy)
      (Sign.classes_of thy);
    fun classrel (l as Lookup (classes, p), _) class  =
          Lookup (class :: classes, p)
      | classrel (Instance ((_, tyco), lss), _) class =
          Instance ((class, tyco), lss);
    fun constructor tyco lss class =
      Instance ((class, tyco), (map o map) fst lss)
    fun variable (TFree (v, sort)) =
          map_index (fn (n, class) => (Lookup ([], (v, (n, length sort))), class))
            (operational_sort_of thy sort)
      | variable (TVar _) = error "TVar encountered while deriving sortlookup";
  in
    Sorts.of_sort_derivation pp algebra
      {classrel = classrel, constructor = constructor, variable = variable}
      (typ_ctxt, operational_sort_of thy sort_decl)
  end;

fun sortlookups_const thy (c, typ_ctxt) =
  let
    val typ_decl = case AxClass.class_of_param thy c
     of NONE => Sign.the_const_type thy c
      | SOME class => case the_consts_sign thy class of (v, cs) =>
          (Logic.legacy_varifyT o subst_clsvar v (TFree (v, [class])))
          ((the o AList.lookup (op =) cs) c)
  in
    instantiations_of thy (typ_decl, typ_ctxt)
    |> the
    |> map (fn ((_, sort), ty) => sortlookup thy (sort, ty))
    |> filter_out null
  end;


(* toplevel interface *)

local

structure P = OuterParse
and K = OuterKeyword

in

val (classK, instanceK) = ("class", "instance")

fun wrap_add_instance_sort ((class, sort), use_interp) thy =
  if use_interp
    andalso forall (is_some o lookup_class_data thy) (Sign.read_sort thy sort)
  then
    instance_sort (class, sort) thy
  else
    axclass_instance_sort (class, sort) thy;

val parse_inst =
  (Scan.optional (P.$$$ "(" |-- P.!!! (P.list1 P.sort --| P.$$$ ")")) [] -- P.xname --| P.$$$ "::" -- P.sort)
    >> (fn ((asorts, tyco), sort) => ((tyco, asorts), sort))
  || (P.xname --| P.$$$ "::" -- P.!!! P.arity)
    >> (fn (tyco, (asorts, sort)) => ((tyco, asorts), sort));

val locale_val =
  (P.locale_expr --
    Scan.optional (P.$$$ "+" |-- P.!!! (Scan.repeat1 P.context_element)) [] ||
  Scan.repeat1 P.context_element >> pair Locale.empty);

val class_subP = P.name -- Scan.repeat (P.$$$ "+" |-- P.name) >> (op ::);
val class_bodyP = P.!!! (Scan.repeat1 P.context_element);

val classP =
  OuterSyntax.command classK "operational type classes" K.thy_decl (
    P.name --| P.$$$ "="
    -- (
      class_subP --| P.$$$ "+" -- class_bodyP
      || class_subP >> rpair []
      || class_bodyP >> pair []
    ) >> (Toplevel.theory_context
          o (fn (bname, (supclasses, elems)) => class bname supclasses elems)));

val instanceP =
  OuterSyntax.command instanceK "prove type arity or subclass relation" K.thy_goal ((
      P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.!!! P.xname) -- P.opt_keyword "open" >> wrap_add_instance_sort
      || P.opt_thm_name ":" -- (P.and_list1 parse_inst -- Scan.repeat (P.opt_thm_name ":" -- P.prop))
           >> (fn (("", []), ([((tyco, asorts), sort)], [])) => axclass_instance_arity I [(tyco, asorts, sort)]
                | (natts, (arities, defs)) => instance_arity arities natts defs)
    ) >> (Toplevel.print oo Toplevel.theory_to_proof));

val _ = OuterSyntax.add_parsers [classP, instanceP];

end; (* local *)

end; (* struct *)