src/Pure/axclass.ML
author wenzelm
Thu Oct 04 20:29:42 2007 +0200 (2007-10-04)
changeset 24850 0cfd722ab579
parent 24847 bc15dcaed517
child 24920 2a45e400fdad
permissions -rw-r--r--
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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 as parameter records and predicates, with explicit
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definitions and proofs.
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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 define_class_params: bstring * class list -> ((bstring * typ) * mixfix) list ->
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    (theory -> (string * typ) list -> ((bstring * attribute list) * term list) list) ->
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    string list -> theory ->
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    (class * ((string * typ) list * thm list)) * 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_definition: theory -> class -> {def: thm, intro: thm, axioms: thm list,
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    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 params_of_class: theory -> class -> string * (string * typ) list
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  val print_axclasses: theory -> unit
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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 * xstring list -> theory -> theory
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  val axiomatize_class_i: bstring * class list -> theory -> theory
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  val axiomatize_classrel: (xstring * xstring) list -> theory -> theory
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  val axiomatize_classrel_i: (class * class) list -> theory -> theory
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  val axiomatize_arity: xstring * string list * string -> theory -> theory
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  val axiomatize_arity_i: arity -> theory -> theory
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  type cache
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  val cache: cache
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  val of_sort: theory -> typ * sort -> cache -> thm list * cache  (*exception Sorts.CLASS_ERROR*)
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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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(* setup data *)
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structure AxClassData = TheoryDataFun
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(
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  type T = axclasses * instances;
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  val 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), (axclasses2, instances2)) =
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    (merge_axclasses pp (axclasses1, axclasses2), (merge_instances (instances1, instances2)));
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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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fun map_axclasses f = AxClassData.map (apfst f);
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val lookup_def = Symtab.lookup o #1 o get_axclasses;
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fun get_definition 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 =
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  AList.lookup (op =) (#2 (get_axclasses thy));
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fun params_of_class thy class = (Name.aT, #params (get_definition thy class));
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(* maintain instances *)
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val get_instances = #2 o AxClassData.get;
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fun map_instances f = AxClassData.map (apsnd f);
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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 " ^ Sign.string_of_classrel 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 " ^ Sign.string_of_arity 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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(* print data *)
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fun print_axclasses thy =
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  let
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    val axclasses = #1 (get_axclasses thy);
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    val ctxt = ProofContext.init thy;
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    fun pretty_axclass (class, AxClass {def, intro, axioms, params}) =
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      Pretty.block (Pretty.fbreaks
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       [Pretty.block
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          [Pretty.str "class ", ProofContext.pretty_sort ctxt [class], Pretty.str ":"],
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        Pretty.strs ("parameters:" :: params_of thy class),
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        ProofContext.pretty_fact ctxt ("def", [def]),
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        ProofContext.pretty_fact ctxt (introN, [intro]),
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        ProofContext.pretty_fact ctxt (axiomsN, axioms)]);
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  in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses))) end;
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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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  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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  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 (c1, c2) = cert_classrel thy raw_rel;
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    val th = Goal.prove (ProofContext.init thy) [] []
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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 (Sign.string_of_classrel thy [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 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 (ProofContext.init thy) [] [] 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 (Sign.string_of_arity thy 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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(** class definitions **)
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fun split_defined n eq =
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  let
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    val intro =
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      (eq RS Drule.equal_elim_rule2)
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      |> Conjunction.curry_balanced n
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      |> n = 0 ? Thm.eq_assumption 1;
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    val dests =
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      if n = 0 then []
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      else
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        (eq RS Drule.equal_elim_rule1)
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        |> BalancedTree.dest (fn th =>
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          (th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
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  in (intro, dests) end;
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fun define_class (bclass, raw_super) params raw_specs thy =
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  let
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    val ctxt = ProofContext.init thy;
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    val pp = ProofContext.pp ctxt;
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    (* prepare specification *)
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    val bconst = Logic.const_of_class bclass;
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    val class = Sign.full_name thy bclass;
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    val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
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    fun prep_axiom t =
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      (case Term.add_tfrees t [] of
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        [(a, S)] =>
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          if Sign.subsort thy (super, S) then t
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          else error ("Sort constraint of type variable " ^
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            setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
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            " needs to be weaker than " ^ Pretty.string_of_sort pp super)
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      | [] => t
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      | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t))
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      |> map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
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      |> Logic.close_form;
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    val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
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    val name_atts = map fst raw_specs;
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    (* definition *)
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    val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss;
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    val class_eq =
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      Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
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    val ([def], def_thy) =
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      thy
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      |> Sign.primitive_class (bclass, super)
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      |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
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    val (raw_intro, (raw_classrel, raw_axioms)) =
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      split_defined (length conjs) def ||> chop (length super);
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    (* facts *)
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    val class_triv = Thm.class_triv def_thy class;
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    val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
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      def_thy
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      |> PureThy.note_thmss_qualified "" bconst
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        [((introN, []), [([Drule.standard raw_intro], [])]),
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         ((superN, []), [(map Drule.standard raw_classrel, [])]),
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         ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])];
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    (* params *)
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    val params_typs = map (fn param =>
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      let
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        val ty = Sign.the_const_type thy param;
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   337
        val _ = case Term.typ_tvars ty
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   338
         of [_] => ()
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   339
          | _ => error ("Exactly one type variable required in parameter " ^ quote param);
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   340
        val ty' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) ty;
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   341
      in (param, ty') end) params;
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   342
wenzelm@24847
   343
wenzelm@19511
   344
    (* result *)
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   345
haftmann@21925
   346
    val axclass = make_axclass ((def, intro, axioms), params_typs);
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   347
    val result_thy =
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   348
      facts_thy
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   349
      |> fold put_classrel (map (pair class) super ~~ classrel)
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   350
      |> Sign.add_path bconst
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   351
      |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
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   352
      |> Sign.restore_naming facts_thy
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   353
      |> map_axclasses (fn (axclasses, parameters) =>
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        (Symtab.update (class, axclass) axclasses,
wenzelm@19574
   355
          fold (fn x => add_param pp (x, class)) params parameters));
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   356
wenzelm@19511
   357
  in (class, result_thy) end;
wenzelm@19511
   358
wenzelm@19511
   359
wenzelm@19531
   360
haftmann@24589
   361
(** axclasses with implicit parameter handling **)
haftmann@24589
   362
haftmann@24589
   363
fun define_class_params (name, raw_superclasses) raw_consts raw_dep_axioms other_consts thy =
haftmann@24589
   364
  let
haftmann@24589
   365
    val superclasses = map (Sign.certify_class thy) raw_superclasses;
haftmann@24589
   366
    val consts = (map o apfst o apsnd) (Sign.certify_typ thy) raw_consts;
haftmann@24589
   367
    val prefix = Logic.const_of_class name;
haftmann@24589
   368
    fun mk_const_name c = NameSpace.map_base (NameSpace.append prefix)
haftmann@24589
   369
      (Sign.full_name thy c);
haftmann@24589
   370
    fun add_const ((c, ty), syn) =
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   371
      Sign.add_consts_authentic [] [(c, ty, syn)]
haftmann@24589
   372
      #> pair (mk_const_name c, ty);
haftmann@24589
   373
    fun mk_axioms cs thy =
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   374
      raw_dep_axioms thy cs
haftmann@24589
   375
      |> (map o apsnd o map) (Sign.cert_prop thy)
haftmann@24589
   376
      |> rpair thy;
haftmann@24589
   377
    fun add_constraint class (c, ty) =
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   378
      Sign.add_const_constraint (c, SOME
haftmann@24589
   379
        (Term.map_type_tfree (fn (v, _) => TFree (v, [class])) ty));
haftmann@24589
   380
  in
haftmann@24589
   381
    thy
wenzelm@24712
   382
    |> Sign.add_path prefix
haftmann@24589
   383
    |> fold_map add_const consts
wenzelm@24712
   384
    ||> Sign.restore_naming thy
haftmann@24589
   385
    |-> (fn cs => mk_axioms cs
haftmann@24589
   386
    #-> (fn axioms_prop => define_class (name, superclasses)
haftmann@24589
   387
           (map fst cs @ other_consts) axioms_prop
haftmann@24589
   388
    #-> (fn class => `(fn thy => get_definition thy class)
haftmann@24589
   389
    #-> (fn {axioms, ...} => fold (add_constraint class) cs
haftmann@24589
   390
    #> pair (class, (cs, axioms))))))
haftmann@24589
   391
  end;
haftmann@24589
   392
haftmann@24589
   393
haftmann@24589
   394
wenzelm@19511
   395
(** axiomatizations **)
wenzelm@19511
   396
wenzelm@19511
   397
local
wenzelm@19511
   398
wenzelm@20628
   399
fun axiomatize prep mk name add raw_args thy =
wenzelm@20628
   400
  let
wenzelm@20628
   401
    val args = prep thy raw_args;
wenzelm@20628
   402
    val specs = mk args;
wenzelm@20628
   403
    val names = name args;
wenzelm@20628
   404
  in thy |> PureThy.add_axioms_i (map (rpair []) (names ~~ specs)) |-> fold add end;
wenzelm@19511
   405
wenzelm@19511
   406
fun ax_classrel prep =
wenzelm@20628
   407
  axiomatize (map o prep) (map Logic.mk_classrel)
wenzelm@20628
   408
    (map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
wenzelm@19511
   409
wenzelm@19511
   410
fun ax_arity prep =
wenzelm@20628
   411
  axiomatize prep Logic.mk_arities
wenzelm@20628
   412
    (map (prefix arity_prefix) o Logic.name_arities) add_arity;
wenzelm@19511
   413
wenzelm@19706
   414
fun class_const c =
wenzelm@19706
   415
  (Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
wenzelm@19706
   416
wenzelm@19511
   417
fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
wenzelm@19511
   418
  let
wenzelm@19511
   419
    val class = Sign.full_name thy bclass;
wenzelm@24731
   420
    val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
wenzelm@19511
   421
  in
wenzelm@19511
   422
    thy
wenzelm@19511
   423
    |> Sign.primitive_class (bclass, super)
wenzelm@19511
   424
    |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
wenzelm@19706
   425
    |> Theory.add_deps "" (class_const class) (map class_const super)
wenzelm@19511
   426
  end;
wenzelm@19511
   427
wenzelm@19511
   428
in
wenzelm@19511
   429
wenzelm@19511
   430
val axiomatize_class = ax_class Sign.read_class read_classrel;
wenzelm@19511
   431
val axiomatize_class_i = ax_class Sign.certify_class cert_classrel;
wenzelm@19511
   432
val axiomatize_classrel = ax_classrel read_classrel;
wenzelm@19511
   433
val axiomatize_classrel_i = ax_classrel cert_classrel;
wenzelm@19511
   434
val axiomatize_arity = ax_arity Sign.read_arity;
wenzelm@19511
   435
val axiomatize_arity_i = ax_arity Sign.cert_arity;
wenzelm@19511
   436
wenzelm@19511
   437
end;
wenzelm@19511
   438
wenzelm@19511
   439
wenzelm@19511
   440
wenzelm@19511
   441
(** explicit derivations -- cached **)
wenzelm@19511
   442
wenzelm@19574
   443
datatype cache = Types of (class * thm) list Typtab.table;
wenzelm@19574
   444
val cache = Types Typtab.empty;
wenzelm@19574
   445
wenzelm@19511
   446
local
wenzelm@19503
   447
wenzelm@19574
   448
fun lookup_type (Types cache) = AList.lookup (op =) o Typtab.lookup_list cache;
wenzelm@19574
   449
fun insert_type T der (Types cache) = Types (Typtab.insert_list (eq_fst op =) (T, der) cache);
wenzelm@19503
   450
wenzelm@19522
   451
fun derive_type _ (_, []) = []
wenzelm@19522
   452
  | derive_type thy (typ, sort) =
wenzelm@19522
   453
      let
wenzelm@19528
   454
        val vars = Term.fold_atyps
wenzelm@19522
   455
            (fn T as TFree (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19522
   456
              | T as TVar (_, S) => insert (eq_fst op =) (T, S)
wenzelm@19528
   457
              | _ => I) typ [];
wenzelm@19574
   458
        val hyps = vars
wenzelm@19574
   459
          |> map (fn (T, S) => (T, Drule.sort_triv thy (T, S) ~~ S));
wenzelm@19642
   460
        val ths = (typ, sort) |> Sorts.of_sort_derivation (Sign.pp thy) (Sign.classes_of thy)
wenzelm@22570
   461
           {class_relation =
wenzelm@19574
   462
              fn (th, c1) => fn c2 => th RS the_classrel thy (c1, c2),
wenzelm@22570
   463
            type_constructor =
wenzelm@19574
   464
              fn a => fn dom => fn c =>
wenzelm@19574
   465
                let val Ss = map (map snd) dom and ths = maps (map fst) dom
wenzelm@19574
   466
                in ths MRS the_arity thy a (c, Ss) end,
wenzelm@22570
   467
            type_variable =
wenzelm@19574
   468
              the_default [] o AList.lookup (op =) hyps};
wenzelm@19574
   469
      in ths end;
wenzelm@19503
   470
wenzelm@19511
   471
in
wenzelm@19511
   472
wenzelm@19574
   473
fun of_sort thy (typ, sort) cache =
wenzelm@19574
   474
  let
wenzelm@19574
   475
    val sort' = filter (is_none o lookup_type cache typ) sort;
wenzelm@19574
   476
    val ths' = derive_type thy (typ, sort')
wenzelm@19574
   477
      handle ERROR msg => cat_error msg ("The error(s) above occurred for sort derivation: " ^
wenzelm@19574
   478
        Sign.string_of_typ thy typ ^ " :: " ^ Sign.string_of_sort thy sort');
wenzelm@19574
   479
    val cache' = cache |> fold (insert_type typ) (sort' ~~ ths');
wenzelm@19574
   480
    val ths =
wenzelm@19574
   481
      sort |> map (fn c =>
wenzelm@19574
   482
        Goal.finish (the (lookup_type cache' typ c) RS
wenzelm@19574
   483
          Goal.init (Thm.cterm_of thy (Logic.mk_inclass (typ, c))))
wenzelm@20260
   484
        |> Thm.adjust_maxidx_thm ~1);
wenzelm@19574
   485
  in (ths, cache') end;
wenzelm@19503
   486
wenzelm@19511
   487
end;
wenzelm@19418
   488
wenzelm@15876
   489
end;