src/Pure/axclass.ML
author haftmann
Tue Dec 11 10:23:12 2007 +0100 (2007-12-11)
changeset 25605 35a5f7f4b97b
parent 25597 34860182b250
child 25617 b495384e48e1
permissions -rw-r--r--
error handling for pathological cases
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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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Type classes defined as predicates, associated with a record of
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parameters.
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*)
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signature AX_CLASS =
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sig
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  val define_class: bstring * class list -> string list ->
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    ((bstring * attribute list) * term list) list -> theory -> class * theory
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  val add_classrel: thm -> theory -> theory
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  val add_arity: thm -> theory -> theory
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  val prove_classrel: class * class -> tactic -> theory -> theory
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  val prove_arity: string * sort list * sort -> tactic -> theory -> theory
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  val get_info: theory -> class ->
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    {def: thm, intro: thm, axioms: thm list, params: (string * typ) list}
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  val class_intros: theory -> thm list
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  val class_of_param: theory -> string -> class option
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  val cert_classrel: theory -> class * class -> class * class
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  val read_classrel: theory -> xstring * xstring -> class * class
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  val axiomatize_class: bstring * class list -> theory -> theory
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  val axiomatize_class_cmd: bstring * xstring list -> theory -> theory
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  val axiomatize_classrel: (class * class) list -> theory -> theory
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  val axiomatize_classrel_cmd: (xstring * xstring) list -> theory -> theory
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  val axiomatize_arity: arity -> theory -> theory
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  val axiomatize_arity_cmd: xstring * string list * string -> theory -> theory
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  val instance_name: string * class -> string
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  val declare_overloaded: string * typ -> theory -> term * theory
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  val define_overloaded: string -> string * term -> theory -> thm * theory
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  val inst_tyco_of: theory -> string * typ -> string option
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  val unoverload: theory -> thm -> thm
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  val overload: theory -> thm -> thm
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  val unoverload_conv: theory -> conv
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  val overload_conv: theory -> conv
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  val unoverload_const: theory -> string * typ -> string
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  val param_of_inst: theory -> string * string -> string
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  val inst_of_param: theory -> string -> (string * string) option
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  type cache
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  val of_sort: theory -> typ * sort -> cache -> thm list * cache  (*exception Sorts.CLASS_ERROR*)
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  val cache: cache
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end;
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structure AxClass: AX_CLASS =
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struct
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(** theory data **)
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(* class parameters (canonical order) *)
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type param = string * class;
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fun add_param pp ((x, c): param) params =
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  (case AList.lookup (op =) params x of
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    NONE => (x, c) :: params
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  | SOME c' => error ("Duplicate class parameter " ^ quote x ^
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      " for " ^ Pretty.string_of_sort pp [c] ^
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      (if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
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fun merge_params _ ([], qs) = qs
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  | merge_params pp (ps, qs) =
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      fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
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(* axclasses *)
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val introN = "intro";
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val superN = "super";
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val axiomsN = "axioms";
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datatype axclass = AxClass of
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 {def: thm,
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  intro: thm,
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  axioms: thm list,
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  params: (string * typ) list};
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type axclasses = axclass Symtab.table * param list;
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fun make_axclass ((def, intro, axioms), params) =
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  AxClass {def = def, intro = intro, axioms = axioms, params = params};
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fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
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  (Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
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(* instances *)
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val classrel_prefix = "classrel_";
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val arity_prefix = "arity_";
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type instances =
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  ((class * class) * thm) list *
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  ((class * sort list) * thm) list Symtab.table;
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fun merge_instances ((classrel1, arities1): instances, (classrel2, arities2)) =
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 (merge (eq_fst op =) (classrel1, classrel2),
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  Symtab.join (K (merge (eq_fst op =))) (arities1, arities2));
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(* instance parameters *)
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type inst_params =
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  (string * thm) Symtab.table Symtab.table
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    (*constant name ~> type constructor ~> (constant name, equation)*)
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  * (string * string) Symtab.table; (*constant name ~> (constant name, type constructor)*)
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fun merge_inst_params ((const_param1, param_const1), (const_param2, param_const2)) =
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  (Symtab.join  (K (Symtab.merge (K true))) (const_param1, const_param2),
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    Symtab.merge (K true) (param_const1, param_const2));
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(* setup data *)
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structure AxClassData = TheoryDataFun
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(
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  type T = axclasses * (instances * inst_params);
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  val empty = ((Symtab.empty, []), (([], Symtab.empty), (Symtab.empty, Symtab.empty)));
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  val copy = I;
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  val extend = I;
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  fun merge pp ((axclasses1, (instances1, inst_params1)), (axclasses2, (instances2, inst_params2))) =
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    (merge_axclasses pp (axclasses1, axclasses2),
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      (merge_instances (instances1, instances2), merge_inst_params (inst_params1, inst_params2)));
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);
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(* maintain axclasses *)
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val get_axclasses = #1 o AxClassData.get;
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val map_axclasses = AxClassData.map o apfst;
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val lookup_def = Symtab.lookup o #1 o get_axclasses;
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fun get_info thy c =
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  (case lookup_def thy c of
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    SOME (AxClass info) => info
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  | NONE => error ("No such axclass: " ^ quote c));
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fun class_intros thy =
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  let
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    fun add_intro c =
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      (case lookup_def thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
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    val classes = Sign.all_classes thy;
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  in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
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fun get_params thy pred =
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  let val params = #2 (get_axclasses thy);
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  in fold (fn (x, c) => if pred c then cons x else I) params [] end;
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fun params_of thy c = get_params thy (fn c' => c' = c);
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fun all_params_of thy S = get_params thy (fn c => Sign.subsort thy (S, [c]));
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fun class_of_param thy = AList.lookup (op =) (#2 (get_axclasses thy));
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(* maintain instances *)
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fun instance_name (a, c) = NameSpace.base c ^ "_" ^ NameSpace.base a;
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val get_instances = #1 o #2 o AxClassData.get;
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val map_instances = AxClassData.map o apsnd o apfst;
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fun the_classrel thy (c1, c2) =
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  (case AList.lookup (op =) (#1 (get_instances thy)) (c1, c2) of
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    SOME th => Thm.transfer thy th
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  | NONE => error ("Unproven class relation " ^
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      Syntax.string_of_classrel (ProofContext.init thy) [c1, c2]));
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fun put_classrel arg = map_instances (fn (classrel, arities) =>
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  (insert (eq_fst op =) arg classrel, arities));
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fun the_arity thy a (c, Ss) =
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  (case AList.lookup (op =) (Symtab.lookup_list (#2 (get_instances thy)) a) (c, Ss) of
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    SOME th => Thm.transfer thy th
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  | NONE => error ("Unproven type arity " ^
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      Syntax.string_of_arity (ProofContext.init thy) (a, Ss, [c])));
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fun put_arity ((t, Ss, c), th) = map_instances (fn (classrel, arities) =>
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  (classrel, arities |> Symtab.insert_list (eq_fst op =) (t, ((c, Ss), th))));
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(* maintain instance parameters *)
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val get_inst_params = #2 o #2 o AxClassData.get;
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val map_inst_params = AxClassData.map o apsnd o apsnd;
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fun get_inst_param thy (c, tyco) =
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  (the o Symtab.lookup ((the o Symtab.lookup (fst (get_inst_params thy))) c)) tyco;
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fun add_inst_param (c, tyco) inst = (map_inst_params o apfst
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      o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
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  #> (map_inst_params o apsnd) (Symtab.update_new (fst inst, (c, tyco)));
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val inst_of_param = Symtab.lookup o snd o get_inst_params;
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val param_of_inst = fst oo get_inst_param;
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fun inst_thms thy = (Symtab.fold (Symtab.fold (cons o snd o snd) o snd) o fst)
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  (get_inst_params thy) [];
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val inst_tyco_of = Option.map fst o try (dest_Type o the_single) oo Sign.const_typargs;
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fun unoverload thy = MetaSimplifier.simplify true (inst_thms thy);
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fun overload thy = MetaSimplifier.simplify true (map Thm.symmetric (inst_thms thy));
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fun unoverload_conv thy = MetaSimplifier.rewrite true (inst_thms thy);
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fun overload_conv thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));
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fun unoverload_const thy (c_ty as (c, _)) =
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  case class_of_param thy c
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   of SOME class => (case inst_tyco_of thy c_ty
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       of SOME tyco => try (param_of_inst thy) (c, tyco) |> the_default c
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        | NONE => c)
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    | NONE => c;
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(** instances **)
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(* class relations *)
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fun cert_classrel thy raw_rel =
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  let
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    val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
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    val _ = Sign.primitive_classrel (c1, c2) (Theory.copy thy);
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    val _ =
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      (case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of
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        [] => ()
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      | xs => raise TYPE ("Class " ^ Sign.string_of_sort thy [c1] ^ " lacks parameter(s) " ^
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          commas_quote xs ^ " of " ^ Sign.string_of_sort thy [c2], [], []));
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  in (c1, c2) end;
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fun read_classrel thy raw_rel =
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  cert_classrel thy (pairself (Sign.read_class thy) raw_rel)
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    handle TYPE (msg, _, _) => error msg;
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(* primitive rules *)
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fun add_classrel th thy =
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  let
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    fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
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    val prop = Thm.plain_prop_of (Thm.transfer thy th);
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    val rel = Logic.dest_classrel prop handle TERM _ => err ();
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    val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
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  in
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    thy
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    |> Sign.primitive_classrel (c1, c2)
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    |> put_classrel ((c1, c2), Drule.unconstrainTs th)
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  end;
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fun add_arity th thy =
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  let
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    fun err () = raise THM ("add_arity: malformed type arity", 0, [th]);
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    val prop = Thm.plain_prop_of (Thm.transfer thy th);
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    val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err ();
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    val _ = map (Sign.certify_sort thy) Ss = Ss orelse err ();
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    (*FIXME turn this into a mere check as soon as "attach" has disappeared*)
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    val missing_params = Sign.complete_sort thy [c]
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      |> maps (these o Option.map (fn AxClass { params, ... } => params) o lookup_def thy)
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      |> filter_out (fn (p, _) => can (get_inst_param thy) (p, t));
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    fun declare_missing (p, T0) thy =
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      let
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        val name_inst = instance_name (t, c) ^ "_inst";
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        val p' = NameSpace.base p ^ "_" ^ NameSpace.base t;
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        val vs = Name.names Name.context Name.aT (replicate (Sign.arity_number thy t) []);
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        val T = map_atyps (fn _ => Type (t, map TFree vs)) T0;
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      in
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        thy
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        |> Sign.sticky_prefix name_inst
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        |> Sign.no_base_names
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        |> Sign.declare_const [] (p', T, NoSyn)
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        |-> (fn const' as Const (p'', _) => Thm.add_def false true
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              (Thm.def_name p', Logic.mk_equals (const', Const (p, T)))
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        #>> Thm.varifyT
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        #-> (fn thm => add_inst_param (p, t) (p'', Thm.symmetric thm)
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        #> PureThy.note Thm.internalK (p', thm)
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        #> snd
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        #> Sign.restore_naming thy))
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      end;
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  in
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    thy
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    |> Sign.primitive_arity (t, Ss, [c])
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    |> put_arity ((t, Ss, c), Drule.unconstrainTs th)
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    |> fold declare_missing missing_params
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  end;
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(* tactical proofs *)
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fun prove_classrel raw_rel tac thy =
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  let
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    val ctxt = ProofContext.init thy;
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    val (c1, c2) = cert_classrel thy raw_rel;
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    val th = Goal.prove ctxt [] []
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        (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg =>
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      cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
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        quote (Syntax.string_of_classrel ctxt [c1, c2]));
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  in
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    thy
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    |> PureThy.add_thms [((prefix classrel_prefix (Logic.name_classrel (c1, c2)), th), [])]
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    |-> (fn [th'] => add_classrel th')
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  end;
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fun prove_arity raw_arity tac thy =
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  let
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    val ctxt = ProofContext.init thy;
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    val arity = Sign.cert_arity thy raw_arity;
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    val names = map (prefix arity_prefix) (Logic.name_arities arity);
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    val props = Logic.mk_arities arity;
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    val ths = Goal.prove_multi ctxt [] [] props
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      (fn _ => Goal.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
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        cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
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          quote (Syntax.string_of_arity ctxt arity));
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  in
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    thy
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    |> PureThy.add_thms (map (rpair []) (names ~~ ths))
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    |-> fold add_arity
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  end;
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(* instance parameters and overloaded definitions *)
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haftmann@25597
   326
(* declaration and definition of instances of overloaded constants *)
haftmann@25597
   327
haftmann@25597
   328
fun declare_overloaded (c, T) thy =
haftmann@25597
   329
  let
haftmann@25605
   330
    val class = case class_of_param thy c
haftmann@25605
   331
     of SOME class => class
haftmann@25605
   332
      | NONE => error ("Not a class parameter: " ^ quote c);
haftmann@25605
   333
    val tyco = case inst_tyco_of thy (c, T)
haftmann@25605
   334
     of SOME tyco => tyco
haftmann@25605
   335
      | NONE => error ("Illegal type for instantiation of class parameter: "
haftmann@25605
   336
        ^ quote (c ^ " :: " ^ Sign.string_of_typ thy T));
haftmann@25597
   337
    val name_inst = instance_name (tyco, class) ^ "_inst";
haftmann@25597
   338
    val c' = NameSpace.base c ^ "_" ^ NameSpace.base tyco;
haftmann@25597
   339
    val T' = Type.strip_sorts T;
haftmann@25597
   340
  in
haftmann@25597
   341
    thy
haftmann@25597
   342
    |> Sign.sticky_prefix name_inst
haftmann@25597
   343
    |> Sign.no_base_names
haftmann@25597
   344
    |> Sign.declare_const [] (c', T', NoSyn)
haftmann@25597
   345
    |-> (fn const' as Const (c'', _) => Thm.add_def false true
haftmann@25597
   346
          (Thm.def_name c', Logic.mk_equals (Const (c, T'), const'))
haftmann@25597
   347
    #>> Thm.varifyT
haftmann@25597
   348
    #-> (fn thm => add_inst_param (c, tyco) (c'', thm)
haftmann@25597
   349
    #> PureThy.note Thm.internalK (c', thm)
haftmann@25597
   350
    #> snd
haftmann@25597
   351
    #> Sign.restore_naming thy
haftmann@25597
   352
    #> pair (Const (c, T))))
haftmann@25597
   353
  end;
haftmann@25597
   354
haftmann@25597
   355
fun define_overloaded name (c, t) thy =
haftmann@25597
   356
  let
haftmann@25597
   357
    val T = Term.fastype_of t;
haftmann@25597
   358
    val SOME tyco = inst_tyco_of thy (c, T);
haftmann@25597
   359
    val (c', eq) = get_inst_param thy (c, tyco);
haftmann@25597
   360
    val prop = Logic.mk_equals (Const (c', T), t);
haftmann@25597
   361
    val name' = Thm.def_name_optional
haftmann@25597
   362
      (NameSpace.base c ^ "_" ^ NameSpace.base tyco) name;
haftmann@25597
   363
  in
haftmann@25597
   364
    thy
haftmann@25597
   365
    |> Thm.add_def false false (name', prop)
haftmann@25597
   366
    |>> (fn thm =>  Drule.transitive_thm OF [eq, thm])
haftmann@25597
   367
  end;
haftmann@25597
   368
haftmann@25597
   369
wenzelm@19511
   370
wenzelm@19511
   371
(** class definitions **)
wenzelm@19511
   372
wenzelm@23421
   373
fun split_defined n eq =
wenzelm@23421
   374
  let
wenzelm@23421
   375
    val intro =
wenzelm@23421
   376
      (eq RS Drule.equal_elim_rule2)
wenzelm@23421
   377
      |> Conjunction.curry_balanced n
wenzelm@23421
   378
      |> n = 0 ? Thm.eq_assumption 1;
wenzelm@23421
   379
    val dests =
wenzelm@23421
   380
      if n = 0 then []
wenzelm@23421
   381
      else
wenzelm@23421
   382
        (eq RS Drule.equal_elim_rule1)
wenzelm@23421
   383
        |> BalancedTree.dest (fn th =>
wenzelm@23421
   384
          (th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
wenzelm@23421
   385
  in (intro, dests) end;
wenzelm@23421
   386
wenzelm@24964
   387
fun define_class (bclass, raw_super) raw_params raw_specs thy =
wenzelm@19511
   388
  let
wenzelm@19511
   389
    val ctxt = ProofContext.init thy;
wenzelm@24964
   390
    val pp = Syntax.pp ctxt;
wenzelm@19511
   391
wenzelm@19511
   392
wenzelm@24964
   393
    (* class *)
wenzelm@19511
   394
wenzelm@19511
   395
    val bconst = Logic.const_of_class bclass;
wenzelm@19511
   396
    val class = Sign.full_name thy bclass;
wenzelm@24731
   397
    val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
wenzelm@19511
   398
wenzelm@24964
   399
    fun check_constraint (a, S) =
wenzelm@24964
   400
      if Sign.subsort thy (super, S) then ()
wenzelm@24964
   401
      else error ("Sort constraint of type variable " ^
wenzelm@24964
   402
        setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
wenzelm@24964
   403
        " needs to be weaker than " ^ Pretty.string_of_sort pp super);
wenzelm@24964
   404
wenzelm@24964
   405
wenzelm@24964
   406
    (* params *)
wenzelm@24964
   407
wenzelm@24964
   408
    val params = raw_params |> map (fn p =>
wenzelm@24964
   409
      let
wenzelm@24964
   410
        val T = Sign.the_const_type thy p;
wenzelm@24964
   411
        val _ =
wenzelm@24964
   412
          (case Term.add_tvarsT T [] of
wenzelm@24964
   413
            [((a, _), S)] => check_constraint (a, S)
wenzelm@24964
   414
          | _ => error ("Exactly one type variable expected in class parameter " ^ quote p));
wenzelm@24964
   415
        val T' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) T;
wenzelm@24964
   416
      in (p, T') end);
wenzelm@24964
   417
wenzelm@24964
   418
wenzelm@24964
   419
    (* axioms *)
wenzelm@24964
   420
wenzelm@19511
   421
    fun prep_axiom t =
wenzelm@19511
   422
      (case Term.add_tfrees t [] of
wenzelm@24964
   423
        [(a, S)] => check_constraint (a, S)
wenzelm@24964
   424
      | [] => ()
wenzelm@24964
   425
      | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t);
wenzelm@24964
   426
      t
wenzelm@24964
   427
      |> Term.map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
wenzelm@24964
   428
      |> Logic.close_form);
wenzelm@19511
   429
wenzelm@24681
   430
    val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
haftmann@22745
   431
    val name_atts = map fst raw_specs;
wenzelm@19511
   432
wenzelm@19511
   433
wenzelm@19511
   434
    (* definition *)
wenzelm@19511
   435
wenzelm@19511
   436
    val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss;
wenzelm@19511
   437
    val class_eq =
wenzelm@23421
   438
      Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
wenzelm@19511
   439
wenzelm@19511
   440
    val ([def], def_thy) =
wenzelm@19511
   441
      thy
wenzelm@19511
   442
      |> Sign.primitive_class (bclass, super)
wenzelm@19511
   443
      |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
wenzelm@19511
   444
    val (raw_intro, (raw_classrel, raw_axioms)) =
wenzelm@23421
   445
      split_defined (length conjs) def ||> chop (length super);
wenzelm@19392
   446
wenzelm@19418
   447
wenzelm@19511
   448
    (* facts *)
wenzelm@19511
   449
wenzelm@19511
   450
    val class_triv = Thm.class_triv def_thy class;
wenzelm@19511
   451
    val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
wenzelm@19511
   452
      def_thy
wenzelm@19511
   453
      |> PureThy.note_thmss_qualified "" bconst
wenzelm@19511
   454
        [((introN, []), [([Drule.standard raw_intro], [])]),
wenzelm@19511
   455
         ((superN, []), [(map Drule.standard raw_classrel, [])]),
wenzelm@19511
   456
         ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])];
wenzelm@19511
   457
wenzelm@24847
   458
wenzelm@19511
   459
    (* result *)
wenzelm@19511
   460
wenzelm@24964
   461
    val axclass = make_axclass ((def, intro, axioms), params);
wenzelm@19511
   462
    val result_thy =
wenzelm@19511
   463
      facts_thy
wenzelm@19574
   464
      |> fold put_classrel (map (pair class) super ~~ classrel)
wenzelm@19511
   465
      |> Sign.add_path bconst
wenzelm@19511
   466
      |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
wenzelm@19511
   467
      |> Sign.restore_naming facts_thy
wenzelm@19574
   468
      |> map_axclasses (fn (axclasses, parameters) =>
wenzelm@21919
   469
        (Symtab.update (class, axclass) axclasses,
wenzelm@24964
   470
          fold (fn (x, _) => add_param pp (x, class)) params parameters));
wenzelm@19511
   471
wenzelm@19511
   472
  in (class, result_thy) end;
wenzelm@19511
   473
wenzelm@19511
   474
wenzelm@19531
   475
wenzelm@19511
   476
(** axiomatizations **)
wenzelm@19511
   477
wenzelm@19511
   478
local
wenzelm@19511
   479
wenzelm@20628
   480
fun axiomatize prep mk name add raw_args thy =
wenzelm@20628
   481
  let
wenzelm@20628
   482
    val args = prep thy raw_args;
wenzelm@20628
   483
    val specs = mk args;
wenzelm@20628
   484
    val names = name args;
wenzelm@20628
   485
  in thy |> PureThy.add_axioms_i (map (rpair []) (names ~~ specs)) |-> fold add end;
wenzelm@19511
   486
wenzelm@19511
   487
fun ax_classrel prep =
wenzelm@20628
   488
  axiomatize (map o prep) (map Logic.mk_classrel)
wenzelm@20628
   489
    (map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
wenzelm@19511
   490
wenzelm@19511
   491
fun ax_arity prep =
wenzelm@20628
   492
  axiomatize prep Logic.mk_arities
wenzelm@20628
   493
    (map (prefix arity_prefix) o Logic.name_arities) add_arity;
wenzelm@19511
   494
wenzelm@19706
   495
fun class_const c =
wenzelm@19706
   496
  (Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
wenzelm@19706
   497
wenzelm@19511
   498
fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
wenzelm@19511
   499
  let
wenzelm@19511
   500
    val class = Sign.full_name thy bclass;
wenzelm@24731
   501
    val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
wenzelm@19511
   502
  in
wenzelm@19511
   503
    thy
wenzelm@19511
   504
    |> Sign.primitive_class (bclass, super)
wenzelm@19511
   505
    |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
wenzelm@19706
   506
    |> Theory.add_deps "" (class_const class) (map class_const super)
wenzelm@19511
   507
  end;
wenzelm@19511
   508
wenzelm@19511
   509
in
wenzelm@19511
   510
wenzelm@24929
   511
val axiomatize_class = ax_class Sign.certify_class cert_classrel;
wenzelm@24929
   512
val axiomatize_class_cmd = ax_class Sign.read_class read_classrel;
wenzelm@24929
   513
val axiomatize_classrel = ax_classrel cert_classrel;
wenzelm@24929
   514
val axiomatize_classrel_cmd = ax_classrel read_classrel;
wenzelm@24929
   515
val axiomatize_arity = ax_arity Sign.cert_arity;
wenzelm@24929
   516
val axiomatize_arity_cmd = ax_arity Sign.read_arity;
wenzelm@19511
   517
wenzelm@19511
   518
end;
wenzelm@19511
   519
wenzelm@19511
   520
wenzelm@19511
   521
wenzelm@19511
   522
(** explicit derivations -- cached **)
wenzelm@19511
   523
wenzelm@19574
   524
datatype cache = Types of (class * thm) list Typtab.table;
wenzelm@19574
   525
wenzelm@19511
   526
local
wenzelm@19503
   527
wenzelm@19574
   528
fun lookup_type (Types cache) = AList.lookup (op =) o Typtab.lookup_list cache;
wenzelm@19574
   529
fun insert_type T der (Types cache) = Types (Typtab.insert_list (eq_fst op =) (T, der) cache);
wenzelm@19503
   530
wenzelm@19522
   531
fun derive_type _ (_, []) = []
wenzelm@19522
   532
  | derive_type thy (typ, sort) =
wenzelm@19522
   533
      let
wenzelm@19528
   534
        val vars = Term.fold_atyps
wenzelm@19522
   535
            (fn T as TFree (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19522
   536
              | T as TVar (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19528
   537
              | _ => I) typ [];
wenzelm@19574
   538
        val hyps = vars
wenzelm@19574
   539
          |> map (fn (T, S) => (T, Drule.sort_triv thy (T, S) ~~ S));
wenzelm@19642
   540
        val ths = (typ, sort) |> Sorts.of_sort_derivation (Sign.pp thy) (Sign.classes_of thy)
wenzelm@22570
   541
           {class_relation =
wenzelm@19574
   542
              fn (th, c1) => fn c2 => th RS the_classrel thy (c1, c2),
wenzelm@22570
   543
            type_constructor =
wenzelm@19574
   544
              fn a => fn dom => fn c =>
wenzelm@19574
   545
                let val Ss = map (map snd) dom and ths = maps (map fst) dom
wenzelm@19574
   546
                in ths MRS the_arity thy a (c, Ss) end,
wenzelm@22570
   547
            type_variable =
wenzelm@19574
   548
              the_default [] o AList.lookup (op =) hyps};
wenzelm@19574
   549
      in ths end;
wenzelm@19503
   550
wenzelm@19511
   551
in
wenzelm@19511
   552
wenzelm@19574
   553
fun of_sort thy (typ, sort) cache =
wenzelm@19574
   554
  let
wenzelm@19574
   555
    val sort' = filter (is_none o lookup_type cache typ) sort;
wenzelm@19574
   556
    val ths' = derive_type thy (typ, sort')
wenzelm@19574
   557
      handle ERROR msg => cat_error msg ("The error(s) above occurred for sort derivation: " ^
wenzelm@19574
   558
        Sign.string_of_typ thy typ ^ " :: " ^ Sign.string_of_sort thy sort');
wenzelm@19574
   559
    val cache' = cache |> fold (insert_type typ) (sort' ~~ ths');
wenzelm@19574
   560
    val ths =
wenzelm@19574
   561
      sort |> map (fn c =>
wenzelm@19574
   562
        Goal.finish (the (lookup_type cache' typ c) RS
wenzelm@19574
   563
          Goal.init (Thm.cterm_of thy (Logic.mk_inclass (typ, c))))
wenzelm@20260
   564
        |> Thm.adjust_maxidx_thm ~1);
wenzelm@19574
   565
  in (ths, cache') end;
wenzelm@19503
   566
wenzelm@19511
   567
end;
wenzelm@19418
   568
wenzelm@24929
   569
val cache = Types Typtab.empty;
wenzelm@24929
   570
wenzelm@15876
   571
end;