src/Pure/axclass.ML
author wenzelm
Thu Feb 18 21:26:40 2010 +0100 (2010-02-18 ago)
changeset 35201 c2ddb9395436
parent 35021 c839a4c670c6
child 35238 18ae6ef02fe0
permissions -rw-r--r--
axclass: more precise treatment of naming vs. binding;
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(*  Title:      Pure/axclass.ML
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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: binding * class list -> string list ->
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    (Thm.binding * 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: binding * class list -> theory -> theory
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  val axiomatize_class_cmd: binding * 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: binding -> string * term -> theory -> thm * theory
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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 lookup_inst_param: Consts.T -> ((string * string) * 'a) list -> string * typ -> 'a option
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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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  val thynames_of_arity: theory -> class * string -> string list
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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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  val introN: string
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  val axiomsN: string
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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) = AxClass
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  {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 *  (*classrel theorems*)
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  ((class * sort list) * (thm * string)) list Symtab.table;  (*arity theorems with theory name*)
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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 = Theory_Data_PP
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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 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 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) = Long_Name.base_name c ^ "_" ^ Long_Name.base_name 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 thynames_of_arity thy (c, a) =
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  Symtab.lookup_list (#2 (get_instances thy)) a
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  |> map_filter (fn ((c', _), (_, name)) => if c = c' then SOME name else NONE)
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  |> rev;
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fun insert_arity_completions thy (t, ((c, Ss), (th, thy_name))) arities =
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  let
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    val algebra = Sign.classes_of thy;
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    val super_class_completions =
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      Sign.super_classes thy c
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      |> filter_out (fn c1 => exists (fn ((c2, Ss2), _) => c1 = c2
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          andalso Sorts.sorts_le algebra (Ss2, Ss)) (Symtab.lookup_list arities t));
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    val completions = map (fn c1 => (Sorts.weaken algebra
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      (fn (th, c2) => fn c3 => th RS the_classrel thy (c2, c3)) (th, c) c1
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        |> Thm.close_derivation, c1)) super_class_completions;
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    val arities' = fold (fn (th1, c1) => Symtab.cons_list (t, ((c1, Ss), (th1, thy_name))))
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      completions arities;
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  in (null completions, arities') end;
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fun put_arity ((t, Ss, c), th) thy =
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  let
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    val arity' = (t, ((c, Ss), (th, Context.theory_name thy)));
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  in
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    thy
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    |> map_instances (fn (classrel, arities) => (classrel,
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      arities
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      |> Symtab.insert_list (eq_fst op =) arity'
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      |> insert_arity_completions thy arity'
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      |> snd))
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  end;
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fun complete_arities thy =
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  let
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    val arities = snd (get_instances thy);
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    val (finished, arities') = arities
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      |> fold_map (insert_arity_completions thy) (Symtab.dest_list arities);
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  in
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    if forall I finished then NONE
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    else SOME (thy |> map_instances (fn (classrel, _) => (classrel, arities')))
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  end;
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val _ = Context.>> (Context.map_theory (Theory.at_begin complete_arities));
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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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  case Symtab.lookup ((the_default Symtab.empty o Symtab.lookup (fst (get_inst_params thy))) c) tyco
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   of SOME c' => c'
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    | NONE => error ("No instance parameter for constant " ^ quote c
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        ^ " on type constructor " ^ quote 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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fun get_inst_tyco consts = try (fst o dest_Type o the_single o Consts.typargs consts);
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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 lookup_inst_param consts params (c, T) = case get_inst_tyco consts (c, T)
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 of SOME tyco => AList.lookup (op =) params (c, tyco)
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  | NONE => NONE;
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fun unoverload_const thy (c_ty as (c, _)) =
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  if is_some (class_of_param thy c)
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  then case get_inst_tyco (Sign.consts_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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  else 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 string_of_sort = Syntax.string_of_sort_global thy;
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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 " ^ string_of_sort [c1] ^ " lacks parameter(s) " ^
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          commas_quote xs ^ " of " ^ string_of_sort [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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(* declaration and definition of instances of overloaded constants *)
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fun inst_tyco_of thy (c, T) =
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  (case get_inst_tyco (Sign.consts_of thy) (c, T) of
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    SOME tyco => tyco
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  | NONE => error ("Illegal type for instantiation of class parameter: " ^
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      quote (c ^ " :: " ^ Syntax.string_of_typ_global thy T)));
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fun declare_overloaded (c, T) thy =
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  let
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    val class =
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      (case class_of_param thy c of
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        SOME class => class
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      | NONE => error ("Not a class parameter: " ^ quote c));
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    val tyco = inst_tyco_of thy (c, T);
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    val name_inst = instance_name (tyco, class) ^ "_inst";
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    val c' = Long_Name.base_name c ^ "_" ^ Long_Name.base_name tyco;
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    val T' = Type.strip_sorts T;
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  in
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    thy
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    |> Sign.qualified_path true (Binding.name name_inst)
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    |> Sign.declare_const ((Binding.name c', T'), NoSyn)
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    |-> (fn const' as Const (c'', _) =>
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      Thm.add_def false true
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        (Binding.name (Thm.def_name c'), Logic.mk_equals (Const (c, T'), const'))
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      #>> Thm.varifyT
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      #-> (fn thm => add_inst_param (c, tyco) (c'', thm)
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      #> PureThy.add_thm ((Binding.conceal (Binding.name c'), thm), [])
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      #> snd
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      #> pair (Const (c, T))))
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    ||> Sign.restore_naming thy
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  end;
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fun define_overloaded b (c, t) thy =
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  let
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    val T = Term.fastype_of t;
haftmann@31249
   323
    val tyco = inst_tyco_of thy (c, T);
haftmann@25597
   324
    val (c', eq) = get_inst_param thy (c, tyco);
haftmann@25597
   325
    val prop = Logic.mk_equals (Const (c', T), t);
haftmann@30519
   326
    val b' = Thm.def_binding_optional
haftmann@30519
   327
      (Binding.name (Long_Name.base_name c ^ "_" ^ Long_Name.base_name tyco)) b;
haftmann@25597
   328
  in
haftmann@25597
   329
    thy
haftmann@30519
   330
    |> Thm.add_def false false (b', prop)
haftmann@25597
   331
    |>> (fn thm =>  Drule.transitive_thm OF [eq, thm])
haftmann@25597
   332
  end;
haftmann@25597
   333
haftmann@25597
   334
haftmann@30951
   335
(* primitive rules *)
haftmann@30951
   336
wenzelm@31948
   337
fun add_classrel raw_th thy =
haftmann@30951
   338
  let
wenzelm@31948
   339
    val th = Thm.strip_shyps (Thm.transfer thy raw_th);
wenzelm@31948
   340
    val prop = Thm.plain_prop_of th;
haftmann@30951
   341
    fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
haftmann@30951
   342
    val rel = Logic.dest_classrel prop handle TERM _ => err ();
haftmann@30951
   343
    val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
haftmann@30951
   344
  in
haftmann@30951
   345
    thy
haftmann@30951
   346
    |> Sign.primitive_classrel (c1, c2)
haftmann@30951
   347
    |> put_classrel ((c1, c2), Thm.close_derivation (Drule.unconstrainTs th))
haftmann@30951
   348
    |> perhaps complete_arities
haftmann@30951
   349
  end;
haftmann@30951
   350
wenzelm@31948
   351
fun add_arity raw_th thy =
haftmann@30951
   352
  let
wenzelm@31948
   353
    val th = Thm.strip_shyps (Thm.transfer thy raw_th);
wenzelm@31948
   354
    val prop = Thm.plain_prop_of th;
haftmann@30951
   355
    fun err () = raise THM ("add_arity: malformed type arity", 0, [th]);
haftmann@30951
   356
    val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err ();
haftmann@30951
   357
    val T = Type (t, map TFree (Name.names Name.context Name.aT Ss));
haftmann@30951
   358
    val missing_params = Sign.complete_sort thy [c]
haftmann@30951
   359
      |> maps (these o Option.map #params o try (get_info thy))
haftmann@30951
   360
      |> filter_out (fn (const, _) => can (get_inst_param thy) (const, t))
haftmann@30951
   361
      |> (map o apsnd o map_atyps) (K T);
haftmann@30951
   362
    val _ = map (Sign.certify_sort thy) Ss = Ss orelse err ();
haftmann@30951
   363
  in
haftmann@30951
   364
    thy
haftmann@30951
   365
    |> fold (snd oo declare_overloaded) missing_params
haftmann@30951
   366
    |> Sign.primitive_arity (t, Ss, [c])
haftmann@33065
   367
    |> put_arity ((t, Ss, c), Thm.close_derivation (Drule.unconstrainTs th))
haftmann@30951
   368
  end;
haftmann@30951
   369
haftmann@30951
   370
haftmann@30951
   371
(* tactical proofs *)
haftmann@30951
   372
haftmann@30951
   373
fun prove_classrel raw_rel tac thy =
haftmann@30951
   374
  let
haftmann@30951
   375
    val ctxt = ProofContext.init thy;
haftmann@30951
   376
    val (c1, c2) = cert_classrel thy raw_rel;
haftmann@30951
   377
    val th = Goal.prove ctxt [] [] (Logic.mk_classrel (c1, c2)) (K tac) handle ERROR msg =>
haftmann@30951
   378
      cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
haftmann@30951
   379
        quote (Syntax.string_of_classrel ctxt [c1, c2]));
haftmann@30951
   380
  in
haftmann@30951
   381
    thy
haftmann@30951
   382
    |> PureThy.add_thms [((Binding.name
haftmann@30951
   383
        (prefix classrel_prefix (Logic.name_classrel (c1, c2))), th), [])]
haftmann@30951
   384
    |-> (fn [th'] => add_classrel th')
haftmann@30951
   385
  end;
haftmann@30951
   386
haftmann@30951
   387
fun prove_arity raw_arity tac thy =
haftmann@30951
   388
  let
haftmann@30951
   389
    val ctxt = ProofContext.init thy;
haftmann@30951
   390
    val arity = Sign.cert_arity thy raw_arity;
haftmann@30951
   391
    val names = map (prefix arity_prefix) (Logic.name_arities arity);
haftmann@30951
   392
    val props = Logic.mk_arities arity;
haftmann@30951
   393
    val ths = Goal.prove_multi ctxt [] [] props
haftmann@30951
   394
      (fn _ => Goal.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
haftmann@30951
   395
        cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
haftmann@30951
   396
          quote (Syntax.string_of_arity ctxt arity));
haftmann@30951
   397
  in
haftmann@30951
   398
    thy
haftmann@30951
   399
    |> PureThy.add_thms (map (rpair []) (map Binding.name names ~~ ths))
haftmann@30951
   400
    |-> fold add_arity
haftmann@30951
   401
  end;
haftmann@30951
   402
haftmann@30951
   403
wenzelm@19511
   404
wenzelm@19511
   405
(** class definitions **)
wenzelm@19511
   406
wenzelm@23421
   407
fun split_defined n eq =
wenzelm@23421
   408
  let
wenzelm@23421
   409
    val intro =
wenzelm@23421
   410
      (eq RS Drule.equal_elim_rule2)
wenzelm@23421
   411
      |> Conjunction.curry_balanced n
wenzelm@23421
   412
      |> n = 0 ? Thm.eq_assumption 1;
wenzelm@23421
   413
    val dests =
wenzelm@23421
   414
      if n = 0 then []
wenzelm@23421
   415
      else
wenzelm@23421
   416
        (eq RS Drule.equal_elim_rule1)
wenzelm@32765
   417
        |> Balanced_Tree.dest (fn th =>
wenzelm@23421
   418
          (th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
wenzelm@23421
   419
  in (intro, dests) end;
wenzelm@23421
   420
wenzelm@24964
   421
fun define_class (bclass, raw_super) raw_params raw_specs thy =
wenzelm@19511
   422
  let
wenzelm@19511
   423
    val ctxt = ProofContext.init thy;
wenzelm@24964
   424
    val pp = Syntax.pp ctxt;
wenzelm@19511
   425
wenzelm@19511
   426
wenzelm@24964
   427
    (* class *)
wenzelm@19511
   428
wenzelm@30344
   429
    val bconst = Binding.map_name Logic.const_of_class bclass;
wenzelm@30344
   430
    val class = Sign.full_name thy bclass;
wenzelm@24731
   431
    val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
wenzelm@19511
   432
wenzelm@24964
   433
    fun check_constraint (a, S) =
wenzelm@24964
   434
      if Sign.subsort thy (super, S) then ()
wenzelm@24964
   435
      else error ("Sort constraint of type variable " ^
wenzelm@32966
   436
        setmp_CRITICAL show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
wenzelm@24964
   437
        " needs to be weaker than " ^ Pretty.string_of_sort pp super);
wenzelm@24964
   438
wenzelm@24964
   439
wenzelm@24964
   440
    (* params *)
wenzelm@24964
   441
wenzelm@24964
   442
    val params = raw_params |> map (fn p =>
wenzelm@24964
   443
      let
wenzelm@24964
   444
        val T = Sign.the_const_type thy p;
wenzelm@24964
   445
        val _ =
wenzelm@24964
   446
          (case Term.add_tvarsT T [] of
wenzelm@24964
   447
            [((a, _), S)] => check_constraint (a, S)
wenzelm@24964
   448
          | _ => error ("Exactly one type variable expected in class parameter " ^ quote p));
wenzelm@24964
   449
        val T' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) T;
wenzelm@24964
   450
      in (p, T') end);
wenzelm@24964
   451
wenzelm@24964
   452
wenzelm@24964
   453
    (* axioms *)
wenzelm@24964
   454
wenzelm@19511
   455
    fun prep_axiom t =
wenzelm@19511
   456
      (case Term.add_tfrees t [] of
wenzelm@24964
   457
        [(a, S)] => check_constraint (a, S)
wenzelm@24964
   458
      | [] => ()
wenzelm@24964
   459
      | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t);
wenzelm@24964
   460
      t
wenzelm@24964
   461
      |> Term.map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
wenzelm@24964
   462
      |> Logic.close_form);
wenzelm@19511
   463
wenzelm@24681
   464
    val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
haftmann@22745
   465
    val name_atts = map fst raw_specs;
wenzelm@19511
   466
wenzelm@19511
   467
wenzelm@19511
   468
    (* definition *)
wenzelm@19511
   469
wenzelm@31943
   470
    val conjs = map (curry Logic.mk_of_class (Term.aT [])) super @ flat axiomss;
wenzelm@19511
   471
    val class_eq =
wenzelm@31943
   472
      Logic.mk_equals (Logic.mk_of_class (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
wenzelm@19511
   473
wenzelm@19511
   474
    val ([def], def_thy) =
wenzelm@19511
   475
      thy
wenzelm@19511
   476
      |> Sign.primitive_class (bclass, super)
wenzelm@30344
   477
      |> PureThy.add_defs false [((Binding.map_name Thm.def_name bconst, class_eq), [])];
wenzelm@19511
   478
    val (raw_intro, (raw_classrel, raw_axioms)) =
wenzelm@23421
   479
      split_defined (length conjs) def ||> chop (length super);
wenzelm@19392
   480
wenzelm@19418
   481
wenzelm@19511
   482
    (* facts *)
wenzelm@19511
   483
wenzelm@19511
   484
    val class_triv = Thm.class_triv def_thy class;
wenzelm@19511
   485
    val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
wenzelm@19511
   486
      def_thy
wenzelm@35201
   487
      |> Sign.qualified_path true bconst
haftmann@27691
   488
      |> PureThy.note_thmss ""
wenzelm@35021
   489
        [((Binding.name introN, []), [([Drule.export_without_context raw_intro], [])]),
wenzelm@35021
   490
         ((Binding.name superN, []), [(map Drule.export_without_context raw_classrel, [])]),
haftmann@28965
   491
         ((Binding.name axiomsN, []),
wenzelm@35021
   492
           [(map (fn th => Drule.export_without_context (class_triv RS th)) raw_axioms, [])])]
haftmann@27691
   493
      ||> Sign.restore_naming def_thy;
wenzelm@19511
   494
wenzelm@24847
   495
wenzelm@19511
   496
    (* result *)
wenzelm@19511
   497
wenzelm@24964
   498
    val axclass = make_axclass ((def, intro, axioms), params);
wenzelm@19511
   499
    val result_thy =
wenzelm@19511
   500
      facts_thy
wenzelm@19574
   501
      |> fold put_classrel (map (pair class) super ~~ classrel)
wenzelm@35201
   502
      |> Sign.qualified_path false bconst
haftmann@27691
   503
      |> PureThy.note_thmss "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
wenzelm@19511
   504
      |> Sign.restore_naming facts_thy
wenzelm@19574
   505
      |> map_axclasses (fn (axclasses, parameters) =>
wenzelm@21919
   506
        (Symtab.update (class, axclass) axclasses,
wenzelm@24964
   507
          fold (fn (x, _) => add_param pp (x, class)) params parameters));
wenzelm@19511
   508
wenzelm@19511
   509
  in (class, result_thy) end;
wenzelm@19511
   510
wenzelm@19511
   511
wenzelm@19531
   512
wenzelm@19511
   513
(** axiomatizations **)
wenzelm@19511
   514
wenzelm@19511
   515
local
wenzelm@19511
   516
wenzelm@20628
   517
fun axiomatize prep mk name add raw_args thy =
wenzelm@20628
   518
  let
wenzelm@20628
   519
    val args = prep thy raw_args;
wenzelm@20628
   520
    val specs = mk args;
wenzelm@20628
   521
    val names = name args;
haftmann@29579
   522
  in
haftmann@29579
   523
    thy
haftmann@29579
   524
    |> PureThy.add_axioms (map (rpair []) (map Binding.name names ~~ specs))
haftmann@29579
   525
    |-> fold add
haftmann@29579
   526
  end;
wenzelm@19511
   527
wenzelm@19511
   528
fun ax_classrel prep =
wenzelm@20628
   529
  axiomatize (map o prep) (map Logic.mk_classrel)
wenzelm@20628
   530
    (map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
wenzelm@19511
   531
wenzelm@19511
   532
fun ax_arity prep =
wenzelm@20628
   533
  axiomatize prep Logic.mk_arities
wenzelm@20628
   534
    (map (prefix arity_prefix) o Logic.name_arities) add_arity;
wenzelm@19511
   535
wenzelm@19706
   536
fun class_const c =
wenzelm@19706
   537
  (Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
wenzelm@19706
   538
wenzelm@19511
   539
fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
wenzelm@19511
   540
  let
wenzelm@30344
   541
    val class = Sign.full_name thy bclass;
wenzelm@24731
   542
    val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
wenzelm@19511
   543
  in
wenzelm@19511
   544
    thy
wenzelm@19511
   545
    |> Sign.primitive_class (bclass, super)
wenzelm@19511
   546
    |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
wenzelm@19706
   547
    |> Theory.add_deps "" (class_const class) (map class_const super)
wenzelm@19511
   548
  end;
wenzelm@19511
   549
wenzelm@19511
   550
in
wenzelm@19511
   551
wenzelm@24929
   552
val axiomatize_class = ax_class Sign.certify_class cert_classrel;
wenzelm@24929
   553
val axiomatize_class_cmd = ax_class Sign.read_class read_classrel;
wenzelm@24929
   554
val axiomatize_classrel = ax_classrel cert_classrel;
wenzelm@24929
   555
val axiomatize_classrel_cmd = ax_classrel read_classrel;
wenzelm@24929
   556
val axiomatize_arity = ax_arity Sign.cert_arity;
wenzelm@24929
   557
val axiomatize_arity_cmd = ax_arity Sign.read_arity;
wenzelm@19511
   558
wenzelm@19511
   559
end;
wenzelm@19511
   560
wenzelm@19511
   561
wenzelm@19511
   562
wenzelm@19511
   563
(** explicit derivations -- cached **)
wenzelm@19511
   564
wenzelm@19574
   565
datatype cache = Types of (class * thm) list Typtab.table;
wenzelm@19574
   566
wenzelm@19511
   567
local
wenzelm@19503
   568
wenzelm@19574
   569
fun lookup_type (Types cache) = AList.lookup (op =) o Typtab.lookup_list cache;
wenzelm@19574
   570
fun insert_type T der (Types cache) = Types (Typtab.insert_list (eq_fst op =) (T, der) cache);
wenzelm@19503
   571
wenzelm@19522
   572
fun derive_type _ (_, []) = []
wenzelm@19522
   573
  | derive_type thy (typ, sort) =
wenzelm@19522
   574
      let
wenzelm@31944
   575
        val certT = Thm.ctyp_of thy;
wenzelm@19528
   576
        val vars = Term.fold_atyps
wenzelm@19522
   577
            (fn T as TFree (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19522
   578
              | T as TVar (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19528
   579
              | _ => I) typ [];
wenzelm@19574
   580
        val hyps = vars
wenzelm@31944
   581
          |> map (fn (T, S) => (T, Thm.of_sort (certT T, S) ~~ S));
wenzelm@26939
   582
        val ths = (typ, sort)
wenzelm@32791
   583
          |> Sorts.of_sort_derivation (Sign.classes_of thy)
wenzelm@22570
   584
           {class_relation =
wenzelm@19574
   585
              fn (th, c1) => fn c2 => th RS the_classrel thy (c1, c2),
wenzelm@22570
   586
            type_constructor =
wenzelm@19574
   587
              fn a => fn dom => fn c =>
wenzelm@19574
   588
                let val Ss = map (map snd) dom and ths = maps (map fst) dom
wenzelm@19574
   589
                in ths MRS the_arity thy a (c, Ss) end,
wenzelm@22570
   590
            type_variable =
wenzelm@19574
   591
              the_default [] o AList.lookup (op =) hyps};
wenzelm@19574
   592
      in ths end;
wenzelm@19503
   593
wenzelm@19511
   594
in
wenzelm@19511
   595
wenzelm@19574
   596
fun of_sort thy (typ, sort) cache =
wenzelm@19574
   597
  let
wenzelm@19574
   598
    val sort' = filter (is_none o lookup_type cache typ) sort;
wenzelm@19574
   599
    val ths' = derive_type thy (typ, sort')
wenzelm@19574
   600
      handle ERROR msg => cat_error msg ("The error(s) above occurred for sort derivation: " ^
wenzelm@26939
   601
        Syntax.string_of_typ_global thy typ ^ " :: " ^ Syntax.string_of_sort_global thy sort');
wenzelm@19574
   602
    val cache' = cache |> fold (insert_type typ) (sort' ~~ ths');
wenzelm@19574
   603
    val ths =
wenzelm@19574
   604
      sort |> map (fn c =>
wenzelm@32197
   605
        Goal.finish
wenzelm@32197
   606
          (Syntax.init_pretty_global thy)
wenzelm@32197
   607
          (the (lookup_type cache' typ c) RS
wenzelm@32197
   608
            Goal.init (Thm.cterm_of thy (Logic.mk_of_class (typ, c))))
wenzelm@20260
   609
        |> Thm.adjust_maxidx_thm ~1);
wenzelm@19574
   610
  in (ths, cache') end;
wenzelm@19503
   611
wenzelm@19511
   612
end;
wenzelm@19418
   613
wenzelm@24929
   614
val cache = Types Typtab.empty;
wenzelm@24929
   615
wenzelm@15876
   616
end;