src/Pure/Isar/class_declaration.ML
author wenzelm
Sat Dec 14 17:28:05 2013 +0100 (2013-12-14)
changeset 54742 7a86358a3c0b
parent 54740 91f54d386680
child 54866 7b9a67cbd48f
permissions -rw-r--r--
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
clarified tool context in some boundary cases;
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(*  Title:      Pure/Isar/class_declaration.ML
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    Author:     Florian Haftmann, TU Muenchen
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Declaring classes and subclass relations.
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*)
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signature CLASS_DECLARATION =
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sig
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  val class: (local_theory -> local_theory) -> binding -> class list ->
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    Element.context_i list -> theory -> string * local_theory
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  val class_cmd: (local_theory -> local_theory) -> binding -> xstring list ->
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    Element.context list -> theory -> string * local_theory
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  val prove_subclass: (local_theory -> local_theory) -> tactic -> class ->
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    local_theory -> local_theory
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  val subclass: (local_theory -> local_theory) -> class -> local_theory -> Proof.state
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  val subclass_cmd: (local_theory -> local_theory) -> xstring -> local_theory -> Proof.state
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end;
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structure Class_Declaration: CLASS_DECLARATION =
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struct
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(** class definitions **)
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local
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(* calculating class-related rules including canonical interpretation *)
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fun calculate thy class sups base_sort param_map assm_axiom =
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  let
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    val empty_ctxt = Proof_Context.init_global thy;
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    (* instantiation of canonical interpretation *)
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    val aT = TFree (Name.aT, base_sort);
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    val param_map_const = (map o apsnd) Const param_map;
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    val param_map_inst = (map o apsnd)
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      (Const o apsnd (map_atyps (K aT))) param_map;
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    val const_morph = Element.inst_morphism thy
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      (Symtab.empty, Symtab.make param_map_inst);
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    val typ_morph = Element.inst_morphism thy
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      (Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty);
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    val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_ctxt
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      |> Expression.cert_goal_expression ([(class, (("", false),
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           Expression.Named param_map_const))], []);
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    val (props, inst_morph) =
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      if null param_map
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      then (raw_props |> map (Morphism.term typ_morph),
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        raw_inst_morph $> typ_morph)
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      else (raw_props, raw_inst_morph); (*FIXME proper handling in
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        locale.ML / expression.ML would be desirable*)
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    (* witness for canonical interpretation *)
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    val some_prop = try the_single props;
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    val some_witn = Option.map (fn prop =>
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      let
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        val sup_axioms = map_filter (fst o Class.rules thy) sups;
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        val loc_intro_tac =
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          (case Locale.intros_of thy class of
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            (_, NONE) => all_tac
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          | (_, SOME intro) => ALLGOALS (rtac intro));
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        val tac = loc_intro_tac
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          THEN ALLGOALS (Proof_Context.fact_tac empty_ctxt (sup_axioms @ the_list assm_axiom));
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      in Element.prove_witness empty_ctxt prop tac end) some_prop;
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    val some_axiom = Option.map Element.conclude_witness some_witn;
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    (* canonical interpretation *)
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    val base_morph = inst_morph
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      $> Morphism.binding_morphism "class_binding" (Binding.prefix false (Class.class_prefix class))
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      $> Element.satisfy_morphism (the_list some_witn);
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    val eq_morph = Element.eq_morphism thy (Class.these_defs thy sups);
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    (* assm_intro *)
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    fun prove_assm_intro thm =
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      let
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        val ((_, [thm']), _) = Variable.import true [thm] empty_ctxt;
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        val const_eq_morph =
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          (case eq_morph of
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            SOME eq_morph => const_morph $> eq_morph
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          | NONE => const_morph);
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        val thm'' = Morphism.thm const_eq_morph thm';
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      in
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        Goal.prove_sorry_global thy [] [] (Thm.prop_of thm'')
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          (fn {context = ctxt, ...} => ALLGOALS (Proof_Context.fact_tac ctxt [thm'']))
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      end;
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    val some_assm_intro = Option.map prove_assm_intro (fst (Locale.intros_of thy class));
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    (* of_class *)
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    val of_class_prop_concl = Logic.mk_of_class (aT, class);
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    val of_class_prop =
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      (case some_prop of
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        NONE => of_class_prop_concl
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      | SOME prop => Logic.mk_implies (Morphism.term const_morph
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          ((map_types o map_atyps) (K aT) prop), of_class_prop_concl));
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    val sup_of_classes = map (snd o Class.rules thy) sups;
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    val loc_axiom_intros = map Drule.export_without_context_open (Locale.axioms_of thy class);
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    val axclass_intro = #intro (Axclass.get_info thy class);
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    val base_sort_trivs = Thm.of_sort (Thm.ctyp_of thy aT, base_sort);
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    val tac =
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      REPEAT (SOMEGOAL
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        (match_tac (axclass_intro :: sup_of_classes @ loc_axiom_intros @ base_sort_trivs)
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          ORELSE' assume_tac));
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    val of_class = Goal.prove_sorry_global thy [] [] of_class_prop (K tac);
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  in (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) end;
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(* reading and processing class specifications *)
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fun prep_class_elems prep_decl thy sups raw_elems =
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  let
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    (* user space type system: only permits 'a type variable, improves towards 'a *)
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    val algebra = Sign.classes_of thy;
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    val inter_sort = curry (Sorts.inter_sort algebra);
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    val proto_base_sort =
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      if null sups then Sign.defaultS thy
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      else fold inter_sort (map (Class.base_sort thy) sups) [];
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    val base_constraints = (map o apsnd)
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      (map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd)
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        (Class.these_operations thy sups);
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    fun singleton_fixate tms =
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      let
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        val tfrees = fold Term.add_tfrees tms [];
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        val inferred_sort =
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          (fold o fold_types o fold_atyps) (fn TVar (_, S) => inter_sort S | _ => I) tms [];
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        val fixate_sort =
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          (case tfrees of
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            [] => inferred_sort
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          | [(a, S)] =>
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              if a <> Name.aT then
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                error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")
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              else if Sorts.sort_le algebra (S, inferred_sort) then S
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              else
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                error ("Type inference imposes additional sort constraint " ^
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                  Syntax.string_of_sort_global thy inferred_sort ^
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                  " of type parameter " ^ Name.aT ^ " of sort " ^
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                  Syntax.string_of_sort_global thy S)
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          | _ => error "Multiple type variables in class specification");
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        val fixateT = TFree (Name.aT, fixate_sort);
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      in
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        (map o map_types o map_atyps)
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          (fn T as TVar (xi, _) => if Type_Infer.is_param xi then fixateT else T | T => T) tms
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      end;
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    fun after_infer_fixate tms =
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      let
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        val fixate_sort =
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          (fold o fold_types o fold_atyps)
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            (fn TVar (xi, S) => if Type_Infer.is_param xi then inter_sort S else I | _ => I) tms [];
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      in
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        (map o map_types o map_atyps)
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          (fn T as TVar (xi, _) =>
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              if Type_Infer.is_param xi then Type_Infer.param 0 (Name.aT, fixate_sort) else T
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            | T => T) tms
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      end;
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    (* preprocessing elements, retrieving base sort from type-checked elements *)
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    val raw_supexpr =
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      (map (fn sup => (sup, (("", false), Expression.Positional []))) sups, []);
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    val init_class_body =
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      fold (Proof_Context.add_const_constraint o apsnd SOME) base_constraints
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      #> Class.redeclare_operations thy sups
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      #> Context.proof_map (Syntax_Phases.term_check 0 "singleton_fixate" (K singleton_fixate));
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    val ((raw_supparams, _, raw_inferred_elems, _), _) =
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      Proof_Context.init_global thy
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      |> Context.proof_map (Syntax_Phases.term_check 0 "after_infer_fixate" (K after_infer_fixate))
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      |> prep_decl raw_supexpr init_class_body raw_elems;
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    fun filter_element (Element.Fixes []) = NONE
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      | filter_element (e as Element.Fixes _) = SOME e
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      | filter_element (Element.Constrains []) = NONE
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      | filter_element (e as Element.Constrains _) = SOME e
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      | filter_element (Element.Assumes []) = NONE
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      | filter_element (e as Element.Assumes _) = SOME e
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      | filter_element (Element.Defines _) =
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          error ("\"defines\" element not allowed in class specification.")
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      | filter_element (Element.Notes _) =
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          error ("\"notes\" element not allowed in class specification.");
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    val inferred_elems = map_filter filter_element raw_inferred_elems;
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    fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs
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      | fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs
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      | fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) =>
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          fold_types f t #> (fold o fold_types) f ts) o snd) assms;
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    val base_sort =
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      if null inferred_elems then proto_base_sort
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      else
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        (case (fold o fold_element_types) Term.add_tfreesT inferred_elems [] of
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          [] => error "No type variable in class specification"
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        | [(_, sort)] => sort
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        | _ => error "Multiple type variables in class specification");
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    val supparams = map (fn ((c, T), _) =>
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      (c, map_atyps (K (TFree (Name.aT, base_sort))) T)) raw_supparams;
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    val supparam_names = map fst supparams;
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    fun mk_param ((c, _), _) = Free (c, (the o AList.lookup (op =) supparams) c);
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    val supexpr = (map (fn sup => (sup, (("", false),
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      Expression.Positional (map (SOME o mk_param) (Locale.params_of thy sup))))) sups,
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        map (fn (c, T) => (Binding.name c, SOME T, NoSyn)) supparams);
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  in (base_sort, supparam_names, supexpr, inferred_elems) end;
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val cert_class_elems = prep_class_elems Expression.cert_declaration;
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val read_class_elems = prep_class_elems Expression.cert_read_declaration;
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fun prep_class_spec prep_class prep_class_elems thy raw_supclasses raw_elems =
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  let
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    val thy_ctxt = Proof_Context.init_global thy;
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    (* prepare import *)
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    val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
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    val sups = Sign.minimize_sort thy (map (prep_class thy_ctxt) raw_supclasses);
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    val _ =
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      (case filter_out (Class.is_class thy) sups of
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        [] => ()
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      | no_classes => error ("No (proper) classes: " ^ commas_quote no_classes));
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    val raw_supparams = (map o apsnd) (snd o snd) (Class.these_params thy sups);
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    val raw_supparam_names = map fst raw_supparams;
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    val _ =
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      if has_duplicates (op =) raw_supparam_names then
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        error ("Duplicate parameter(s) in superclasses: " ^
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          (commas_quote (duplicates (op =) raw_supparam_names)))
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      else ();
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    (* infer types and base sort *)
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    val (base_sort, supparam_names, supexpr, inferred_elems) = prep_class_elems thy sups raw_elems;
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    val sup_sort = inter_sort base_sort sups;
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    (* process elements as class specification *)
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    val class_ctxt = Class.begin sups base_sort thy_ctxt;
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    val ((_, _, syntax_elems, _), _) = class_ctxt
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      |> Expression.cert_declaration supexpr I inferred_elems;
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    fun check_vars e vs =
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      if null vs then
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        error ("No type variable in part of specification element " ^
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          Pretty.string_of (Pretty.chunks (Element.pretty_ctxt class_ctxt e)))
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      else ();
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    fun check_element (e as Element.Fixes fxs) =
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          List.app (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs
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      | check_element (e as Element.Assumes assms) =
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          List.app (fn (_, ts_pss) =>
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            List.app (fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms
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      | check_element _ = ();
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    val _ = List.app check_element syntax_elems;
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    fun fork_syn (Element.Fixes xs) =
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          fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
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          #>> Element.Fixes
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      | fork_syn x = pair x;
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    val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
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  in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (elems, global_syntax)) end;
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val cert_class_spec = prep_class_spec (K I) cert_class_elems;
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val read_class_spec = prep_class_spec Proof_Context.read_class read_class_elems;
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(* class establishment *)
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fun add_consts class base_sort sups supparam_names global_syntax thy =
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  let
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    (*FIXME simplify*)
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    val supconsts = supparam_names
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      |> AList.make (snd o the o AList.lookup (op =) (Class.these_params thy sups))
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      |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
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    val all_params = Locale.params_of thy class;
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    val raw_params = (snd o chop (length supparam_names)) all_params;
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    fun add_const ((raw_c, raw_ty), _) thy =
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      let
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        val b = Binding.name raw_c;
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        val c = Sign.full_name thy b;
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        val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
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        val ty0 = Type.strip_sorts ty;
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        val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
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        val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;
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      in
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        thy
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        |> Sign.declare_const_global ((b, ty0), syn)
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        |> snd
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        |> pair ((Variable.check_name b, ty), (c, ty'))
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      end;
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  in
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    thy
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    |> Sign.add_path (Class.class_prefix class)
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    |> fold_map add_const raw_params
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    ||> Sign.restore_naming thy
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    |-> (fn params => pair (supconsts @ (map o apfst) fst params, params))
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  end;
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fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy =
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  let
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    (*FIXME simplify*)
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    fun globalize param_map = map_aterms
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      (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
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        | t => t);
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    val raw_pred = Locale.intros_of thy class
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      |> fst
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      |> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of);
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    fun get_axiom thy =
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      (case #axioms (Axclass.get_info thy class) of
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         [] => NONE
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      | [thm] => SOME thm);
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  in
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    thy
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    |> add_consts class base_sort sups supparam_names global_syntax
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    |-> (fn (param_map, params) => Axclass.define_class (bname, supsort)
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          (map (fst o snd) params)
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          [(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)]
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    #> snd
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    #> `get_axiom
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    #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
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    #> pair (param_map, params, assm_axiom)))
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  end;
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fun gen_class prep_class_spec before_exit b raw_supclasses raw_elems thy =
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  let
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    val class = Sign.full_name thy b;
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    val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
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      prep_class_spec thy raw_supclasses raw_elems;
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  in
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    thy
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    |> Expression.add_locale I b (Binding.qualify true "class" b) supexpr elems
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    |> snd |> Local_Theory.exit_global
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    |> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax
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    |-> (fn (param_map, params, assm_axiom) =>
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       `(fn thy => calculate thy class sups base_sort param_map assm_axiom)
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    #-> (fn (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) =>
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       Context.theory_map (Locale.add_registration (class, base_morph)
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         (Option.map (rpair true) eq_morph) export_morph)
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    #> Class.register class sups params base_sort base_morph export_morph some_axiom some_assm_intro of_class))
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    |> Named_Target.init before_exit class
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    |> pair class
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  end;
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in
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val class = gen_class cert_class_spec;
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val class_cmd = gen_class read_class_spec;
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end; (*local*)
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(** subclass relations **)
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local
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fun gen_subclass prep_class do_proof before_exit raw_sup lthy =
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  let
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    val thy = Proof_Context.theory_of lthy;
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    val proto_sup = prep_class thy raw_sup;
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    val proto_sub =
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      (case Named_Target.peek lthy of
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         SOME {target, is_class = true, ...} => target
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      | _ => error "Not in a class target");
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    val (sub, sup) = Axclass.cert_classrel thy (proto_sub, proto_sup);
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    val expr = ([(sup, (("", false), Expression.Positional []))], []);
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    val (([props], deps, export), goal_ctxt) =
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      Expression.cert_goal_expression expr lthy;
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    val some_prop = try the_single props;
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    val some_dep_morph = try the_single (map snd deps);
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    fun after_qed some_wit =
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      Proof_Context.background_theory (Class.register_subclass (sub, sup)
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        some_dep_morph some_wit export)
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      #> Proof_Context.theory_of #> Named_Target.init before_exit sub;
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  in do_proof after_qed some_prop goal_ctxt end;
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fun user_proof after_qed some_prop =
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  Element.witness_proof (after_qed o try the_single o the_single)
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    [the_list some_prop];
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fun tactic_proof tac after_qed some_prop ctxt =
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  after_qed (Option.map
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    (fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;
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in
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val subclass = gen_subclass (K I) user_proof;
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fun prove_subclass before_exit tac = gen_subclass (K I) (tactic_proof tac) before_exit;
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val subclass_cmd = gen_subclass (Proof_Context.read_class o Proof_Context.init_global) user_proof;
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end; (*local*)
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end;