src/HOL/Tools/inductive_set_package.ML
author wenzelm
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(*  Title:      HOL/Tools/inductive_set_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen
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Wrapper for defining inductive sets using package for inductive predicates,
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including infrastructure for converting between predicates and sets.
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*)
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signature INDUCTIVE_SET_PACKAGE =
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sig
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  val to_set_att: thm list -> attribute
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  val to_pred_att: thm list -> attribute
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  val pred_set_conv_att: attribute
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  val add_inductive_i: bool -> bstring -> bool -> bool -> bool ->
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    (string * typ option * mixfix) list ->
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    (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
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      local_theory -> InductivePackage.inductive_result * local_theory
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  val add_inductive: bool -> bool -> (string * string option * mixfix) list ->
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    (string * string option * mixfix) list ->
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    ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
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    local_theory -> InductivePackage.inductive_result * local_theory
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  val setup: theory -> theory
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end;
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structure InductiveSetPackage: INDUCTIVE_SET_PACKAGE =
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struct
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val note_theorem = LocalTheory.note Thm.theoremK;
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(**** simplify {(x1, ..., xn). (x1, ..., xn) : S} to S ****)
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val subset_antisym = thm "subset_antisym";
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val collect_mem_simproc =
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  Simplifier.simproc (theory "Set") "Collect_mem" ["Collect t"] (fn thy => fn ss =>
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    fn S as Const ("Collect", Type ("fun", [_, T])) $ t =>
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         let val (u, Ts, ps) = HOLogic.strip_split t
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         in case u of
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           (c as Const ("op :", _)) $ q $ S' =>
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             (case try (HOLogic.dest_tuple' ps) q of
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                NONE => NONE
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              | SOME ts =>
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                  if not (loose_bvar (S', 0)) andalso
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                    ts = map Bound (length ps downto 0)
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                  then
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                    let val simp = full_simp_tac (Simplifier.inherit_context ss
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                      (HOL_basic_ss addsimps [split_paired_all, split_conv])) 1
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                    in
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                      SOME (Goal.prove (Simplifier.the_context ss) [] []
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                        (Const ("==", T --> T --> propT) $ S $ S')
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                        (K (EVERY
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                          [rtac eq_reflection 1, rtac subset_antisym 1,
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                           rtac subsetI 1, dtac CollectD 1, simp,
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                           rtac subsetI 1, rtac CollectI 1, simp])))
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                    end
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                  else NONE)
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         | _ => NONE
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         end
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     | _ => NONE);
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(***********************************************************************************)
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(* simplifies (%x y. (x, y) : S & P x y) to (%x y. (x, y) : S Int {(x, y). P x y}) *)
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(* and        (%x y. (x, y) : S | P x y) to (%x y. (x, y) : S Un {(x, y). P x y})  *)
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(* used for converting "strong" (co)induction rules                                *)
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(***********************************************************************************)
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val anyt = Free ("t", TFree ("'t", []));
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fun strong_ind_simproc tab =
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  Simplifier.simproc_i HOL.thy "strong_ind" [anyt] (fn thy => fn ss => fn t =>
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    let
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      fun close p t f =
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        let val vs = Term.add_vars t []
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        in Drule.instantiate' [] (rev (map (SOME o cterm_of thy o Var) vs))
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          (p (fold (fn x as (_, T) => fn u => all T $ lambda (Var x) u) vs t) f)
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        end;
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      fun mkop "op &" T x = SOME (Const ("op Int", T --> T --> T), x)
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        | mkop "op |" T x = SOME (Const ("op Un", T --> T --> T), x)
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        | mkop _ _ _ = NONE;
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      fun mk_collect p T t =
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        let val U = HOLogic.dest_setT T
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        in HOLogic.Collect_const U $
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          HOLogic.ap_split' (HOLogic.prod_factors p) U HOLogic.boolT t
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        end;
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      fun decomp (Const (s, _) $ ((m as Const ("op :",
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            Type (_, [_, Type (_, [T, _])]))) $ p $ S) $ u) =
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              mkop s T (m, p, S, mk_collect p T (head_of u))
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        | decomp (Const (s, _) $ u $ ((m as Const ("op :",
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            Type (_, [_, Type (_, [T, _])]))) $ p $ S)) =
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              mkop s T (m, p, mk_collect p T (head_of u), S)
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        | decomp _ = NONE;
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      val simp = full_simp_tac (Simplifier.inherit_context ss
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        (HOL_basic_ss addsimps [mem_Collect_eq, split_conv])) 1;
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      fun mk_rew t = (case strip_abs_vars t of
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          [] => NONE
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        | xs => (case decomp (strip_abs_body t) of
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            NONE => NONE
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          | SOME (bop, (m, p, S, S')) =>
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              SOME (close (Goal.prove (Simplifier.the_context ss) [] [])
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                (Logic.mk_equals (t, list_abs (xs, m $ p $ (bop $ S $ S'))))
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                (K (EVERY
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                  [rtac eq_reflection 1, REPEAT (rtac ext 1), rtac iffI 1,
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                   EVERY [etac conjE 1, rtac IntI 1, simp, simp,
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                     etac IntE 1, rtac conjI 1, simp, simp] ORELSE
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                   EVERY [etac disjE 1, rtac UnI1 1, simp, rtac UnI2 1, simp,
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                     etac UnE 1, rtac disjI1 1, simp, rtac disjI2 1, simp]])))
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                handle ERROR _ => NONE))
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    in
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      case strip_comb t of
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        (h as Const (name, _), ts) => (case Symtab.lookup tab name of
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          SOME _ =>
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            let val rews = map mk_rew ts
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            in
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              if forall is_none rews then NONE
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              else SOME (fold (fn th1 => fn th2 => combination th2 th1)
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                (map2 (fn SOME r => K r | NONE => reflexive o cterm_of thy)
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                   rews ts) (reflexive (cterm_of thy h)))
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            end
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        | NONE => NONE)
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      | _ => NONE
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    end);
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(* only eta contract terms occurring as arguments of functions satisfying p *)
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fun eta_contract p =
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  let
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    fun eta b (Abs (a, T, body)) =
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          (case eta b body of
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             body' as (f $ Bound 0) =>
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               if loose_bvar1 (f, 0) orelse not b then Abs (a, T, body')
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               else incr_boundvars ~1 f
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           | body' => Abs (a, T, body'))
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      | eta b (t $ u) = eta b t $ eta (p (head_of t)) u
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      | eta b t = t
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  in eta false end;
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fun eta_contract_thm p =
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  Conv.fconv_rule (Conv.then_conv (Thm.beta_conversion true, fn ct =>
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    Thm.transitive (Thm.eta_conversion ct)
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      (Thm.symmetric (Thm.eta_conversion
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        (cterm_of (theory_of_cterm ct) (eta_contract p (term_of ct)))))));
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(***********************************************************)
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(* rules for converting between predicate and set notation *)
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(*                                                         *)
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(* rules for converting predicates to sets have the form   *)
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(* P (%x y. (x, y) : s) = (%x y. (x, y) : S s)             *)
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(*                                                         *)
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(* rules for converting sets to predicates have the form   *)
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(* S {(x, y). p x y} = {(x, y). P p x y}                   *)
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(*                                                         *)
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(* where s and p are parameters                            *)
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(***********************************************************)
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structure PredSetConvData = GenericDataFun
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(
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  type T =
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    {(* rules for converting predicates to sets *)
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     to_set_simps: thm list,
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     (* rules for converting sets to predicates *)
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     to_pred_simps: thm list,
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     (* arities of functions of type t set => ... => u set *)
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     set_arities: (typ * (int list list option list * int list list option)) list Symtab.table,
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     (* arities of functions of type (t => ... => bool) => u => ... => bool *)
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     pred_arities: (typ * (int list list option list * int list list option)) list Symtab.table};
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  val empty = {to_set_simps = [], to_pred_simps = [],
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    set_arities = Symtab.empty, pred_arities = Symtab.empty};
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  val extend = I;
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  fun merge _
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    ({to_set_simps = to_set_simps1, to_pred_simps = to_pred_simps1,
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      set_arities = set_arities1, pred_arities = pred_arities1},
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     {to_set_simps = to_set_simps2, to_pred_simps = to_pred_simps2,
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      set_arities = set_arities2, pred_arities = pred_arities2}) =
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    {to_set_simps = Thm.merge_thms (to_set_simps1, to_set_simps2),
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     to_pred_simps = Thm.merge_thms (to_pred_simps1, to_pred_simps2),
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     set_arities = Symtab.merge_list op = (set_arities1, set_arities2),
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     pred_arities = Symtab.merge_list op = (pred_arities1, pred_arities2)};
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);
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fun name_type_of (Free p) = SOME p
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  | name_type_of (Const p) = SOME p
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  | name_type_of _ = NONE;
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fun map_type f (Free (s, T)) = Free (s, f T)
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  | map_type f (Var (ixn, T)) = Var (ixn, f T)
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  | map_type f _ = error "map_type";
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fun find_most_specific is_inst f eq xs T =
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  find_first (fn U => is_inst (T, f U)
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    andalso forall (fn U' => eq (f U, f U') orelse not
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      (is_inst (T, f U') andalso is_inst (f U', f U)))
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        xs) xs;
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fun lookup_arity thy arities (s, T) = case Symtab.lookup arities s of
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    NONE => NONE
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  | SOME xs => find_most_specific (Sign.typ_instance thy) fst (op =) xs T;
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fun lookup_rule thy f rules = find_most_specific
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  (swap #> Pattern.matches thy) (f #> fst) (op aconv) rules;
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fun infer_arities thy arities (optf, t) fs = case strip_comb t of
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    (Abs (s, T, u), []) => infer_arities thy arities (NONE, u) fs
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  | (Abs _, _) => infer_arities thy arities (NONE, Envir.beta_norm t) fs
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  | (u, ts) => (case Option.map (lookup_arity thy arities) (name_type_of u) of
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      SOME (SOME (_, (arity, _))) =>
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        (fold (infer_arities thy arities) (arity ~~ List.take (ts, length arity)) fs
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           handle Subscript => error "infer_arities: bad term")
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    | _ => fold (infer_arities thy arities) (map (pair NONE) ts)
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      (case optf of
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         NONE => fs
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       | SOME f => AList.update op = (u, the_default f
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           (Option.map (curry op inter f) (AList.lookup op = fs u))) fs));
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(**************************************************************)
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(*    derive the to_pred equation from the to_set equation    *)
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(*                                                            *)
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(* 1. instantiate each set parameter with {(x, y). p x y}     *)
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(* 2. apply %P. {(x, y). P x y} to both sides of the equation *)
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(* 3. simplify                                                *)
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(**************************************************************)
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fun mk_to_pred_inst thy fs =
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  map (fn (x, ps) =>
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    let
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      val U = HOLogic.dest_setT (fastype_of x);
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      val x' = map_type (K (HOLogic.prodT_factors' ps U ---> HOLogic.boolT)) x
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    in
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      (cterm_of thy x,
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       cterm_of thy (HOLogic.Collect_const U $
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         HOLogic.ap_split' ps U HOLogic.boolT x'))
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    end) fs;
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fun mk_to_pred_eq p fs optfs' T thm =
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  let
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    val thy = theory_of_thm thm;
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    val insts = mk_to_pred_inst thy fs;
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    val thm' = Thm.instantiate ([], insts) thm;
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    val thm'' = (case optfs' of
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        NONE => thm' RS sym
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      | SOME fs' =>
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          let
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            val U = HOLogic.dest_setT (body_type T);
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            val Ts = HOLogic.prodT_factors' fs' U;
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            (* FIXME: should cterm_instantiate increment indexes? *)
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            val arg_cong' = Thm.incr_indexes (Thm.maxidx_of thm + 1) arg_cong;
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            val (arg_cong_f, _) = arg_cong' |> cprop_of |> Drule.strip_imp_concl |>
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              Thm.dest_comb |> snd |> Drule.strip_comb |> snd |> hd |> Thm.dest_comb
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          in
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            thm' RS (Drule.cterm_instantiate [(arg_cong_f,
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              cterm_of thy (Abs ("P", Ts ---> HOLogic.boolT,
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                HOLogic.Collect_const U $ HOLogic.ap_split' fs' U
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                  HOLogic.boolT (Bound 0))))] arg_cong' RS sym)
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          end)
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  in
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    Simplifier.simplify (HOL_basic_ss addsimps [mem_Collect_eq, split_conv]
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      addsimprocs [collect_mem_simproc]) thm'' |>
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        zero_var_indexes |> eta_contract_thm (equal p)
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  end;
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(**** declare rules for converting predicates to sets ****)
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fun add ctxt thm {to_set_simps, to_pred_simps, set_arities, pred_arities} =
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  case prop_of thm of
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    Const ("Trueprop", _) $ (Const ("op =", Type (_, [T, _])) $ lhs $ rhs) =>
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      (case body_type T of
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         Type ("bool", []) =>
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           let
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             val thy = Context.theory_of ctxt;
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             fun factors_of t fs = case strip_abs_body t of
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                 Const ("op :", _) $ u $ S =>
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                   if is_Free S orelse is_Var S then
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                     let val ps = HOLogic.prod_factors u
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                     in (SOME ps, (S, ps) :: fs) end
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                   else (NONE, fs)
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               | _ => (NONE, fs);
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             val (h, ts) = strip_comb lhs
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             val (pfs, fs) = fold_map factors_of ts [];
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             val ((h', ts'), fs') = (case rhs of
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                 Abs _ => (case strip_abs_body rhs of
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                     Const ("op :", _) $ u $ S =>
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                       (strip_comb S, SOME (HOLogic.prod_factors u))
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                   | _ => error "member symbol on right-hand side expected")
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               | _ => (strip_comb rhs, NONE))
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           in
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             case (name_type_of h, name_type_of h') of
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               (SOME (s, T), SOME (s', T')) =>
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                 (case Symtab.lookup set_arities s' of
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                    NONE => ()
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                  | SOME xs => if exists (fn (U, _) =>
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                        Sign.typ_instance thy (T', U) andalso
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                        Sign.typ_instance thy (U, T')) xs
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                      then
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                        error ("Clash of conversion rules for operator " ^ s')
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                      else ();
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                  {to_set_simps = thm :: to_set_simps,
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                   to_pred_simps =
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                     mk_to_pred_eq h fs fs' T' thm :: to_pred_simps,
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                   set_arities = Symtab.insert_list op = (s',
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                     (T', (map (AList.lookup op = fs) ts', fs'))) set_arities,
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                   pred_arities = Symtab.insert_list op = (s,
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                     (T, (pfs, fs'))) pred_arities})
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             | _ => error "set / predicate constant expected"
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           end
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       | _ => error "equation between predicates expected")
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  | _ => error "equation expected";
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val pred_set_conv_att = Thm.declaration_attribute
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  (fn thm => fn ctxt => PredSetConvData.map (add ctxt thm) ctxt);
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(**** convert theorem in set notation to predicate notation ****)
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fun is_pred tab t =
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  case Option.map (Symtab.lookup tab o fst) (name_type_of t) of
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    SOME (SOME _) => true | _ => false;
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fun to_pred_simproc rules =
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  let val rules' = map mk_meta_eq rules
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  in
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    Simplifier.simproc_i HOL.thy "to_pred" [anyt]
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      (fn thy => K (lookup_rule thy (prop_of #> Logic.dest_equals) rules'))
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  end;
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fun to_pred_proc thy rules t = case lookup_rule thy I rules t of
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    NONE => NONE
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  | SOME (lhs, rhs) =>
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      SOME (Envir.subst_vars
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        (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) rhs);
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fun to_pred thms ctxt thm =
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  let
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    val thy = Context.theory_of ctxt;
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    val {to_pred_simps, set_arities, pred_arities, ...} =
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      fold (add ctxt) thms (PredSetConvData.get ctxt);
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    val fs = filter (is_Var o fst)
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      (infer_arities thy set_arities (NONE, prop_of thm) []);
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    (* instantiate each set parameter with {(x, y). p x y} *)
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    val insts = mk_to_pred_inst thy fs
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  in
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    thm |>
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    Thm.instantiate ([], insts) |>
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    Simplifier.full_simplify (HOL_basic_ss addsimprocs
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      [to_pred_simproc (mem_Collect_eq :: split_conv :: to_pred_simps)]) |>
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    eta_contract_thm (is_pred pred_arities)
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  end;
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val to_pred_att = Thm.rule_attribute o to_pred;
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(**** convert theorem in predicate notation to set notation ****)
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fun to_set thms ctxt thm =
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  let
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    val thy = Context.theory_of ctxt;
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    val {to_set_simps, pred_arities, ...} =
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      fold (add ctxt) thms (PredSetConvData.get ctxt);
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    val fs = filter (is_Var o fst)
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      (infer_arities thy pred_arities (NONE, prop_of thm) []);
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    (* instantiate each predicate parameter with %x y. (x, y) : s *)
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    val insts = map (fn (x, ps) =>
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      let
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        val Ts = binder_types (fastype_of x);
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        val T = HOLogic.mk_tupleT ps Ts;
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        val x' = map_type (K (HOLogic.mk_setT T)) x
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      in
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        (cterm_of thy x,
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         cterm_of thy (list_abs (map (pair "x") Ts, HOLogic.mk_mem
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           (HOLogic.mk_tuple' ps T (map Bound (length ps downto 0)), x'))))
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      end) fs
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  in
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    Simplifier.full_simplify (HOL_basic_ss addsimps to_set_simps
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        addsimprocs [strong_ind_simproc pred_arities])
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      (Thm.instantiate ([], insts) thm)
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  end;
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val to_set_att = Thm.rule_attribute o to_set;
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(**** preprocessor for code generator ****)
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fun codegen_preproc thy =
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  let
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    val {to_pred_simps, set_arities, pred_arities, ...} =
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      PredSetConvData.get (Context.Theory thy);
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    fun preproc thm =
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      if exists_Const (fn (s, _) => case Symtab.lookup set_arities s of
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          NONE => false
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        | SOME arities => exists (fn (_, (xs, _)) =>
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            forall is_none xs) arities) (prop_of thm)
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      then
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        thm |>
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        Simplifier.full_simplify (HOL_basic_ss addsimprocs
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          [to_pred_simproc (mem_Collect_eq :: split_conv :: to_pred_simps)]) |>
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        eta_contract_thm (is_pred pred_arities)
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      else thm
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  in map preproc end;
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fun code_ind_att optmod = to_pred_att [] #> InductiveCodegen.add optmod NONE;
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(**** definition of inductive sets ****)
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fun add_ind_set_def verbose alt_name coind no_elim no_ind cs
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    intros monos params cnames_syn ctxt =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val {set_arities, pred_arities, to_pred_simps, ...} =
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      PredSetConvData.get (Context.Proof ctxt);
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    fun infer (Abs (_, _, t)) = infer t
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      | infer (Const ("op :", _) $ t $ u) =
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          infer_arities thy set_arities (SOME (HOLogic.prod_factors t), u)
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      | infer (t $ u) = infer t #> infer u
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      | infer _ = I;
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    val new_arities = filter_out
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      (fn (x as Free (_, Type ("fun", _)), _) => x mem params
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        | _ => false) (fold (snd #> infer) intros []);
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    val params' = map (fn x => (case AList.lookup op = new_arities x of
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        SOME fs =>
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          let
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            val T = HOLogic.dest_setT (fastype_of x);
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            val Ts = HOLogic.prodT_factors' fs T;
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            val x' = map_type (K (Ts ---> HOLogic.boolT)) x
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          in
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            (x, (x',
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              (HOLogic.Collect_const T $
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                 HOLogic.ap_split' fs T HOLogic.boolT x',
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               list_abs (map (pair "x") Ts, HOLogic.mk_mem
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                 (HOLogic.mk_tuple' fs T (map Bound (length fs downto 0)),
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                  x)))))
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          end
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       | NONE => (x, (x, (x, x))))) params;
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    val (params1, (params2, params3)) =
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      params' |> map snd |> split_list ||> split_list;
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    (* equations for converting sets to predicates *)
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    val ((cs', cs_info), eqns) = cs |> map (fn c as Free (s, T) =>
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      let
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        val fs = the_default [] (AList.lookup op = new_arities c);
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        val U = HOLogic.dest_setT (body_type T);
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        val Ts = HOLogic.prodT_factors' fs U;
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        val c' = Free (s ^ "p",
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          map fastype_of params1 @ Ts ---> HOLogic.boolT)
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      in
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        ((c', (fs, U, Ts)),
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         (list_comb (c, params2),
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          HOLogic.Collect_const U $ HOLogic.ap_split' fs U HOLogic.boolT
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            (list_comb (c', params1))))
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      end) |> split_list |>> split_list;
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    val eqns' = eqns @
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      map (prop_of #> HOLogic.dest_Trueprop #> HOLogic.dest_eq)
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        (mem_Collect_eq :: split_conv :: to_pred_simps);
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    (* predicate version of the introduction rules *)
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    val intros' =
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      map (fn (name_atts, t) => (name_atts,
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        t |>
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        map_aterms (fn u =>
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          (case AList.lookup op = params' u of
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             SOME (_, (u', _)) => u'
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           | NONE => u)) |>
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        Pattern.rewrite_term thy [] [to_pred_proc thy eqns'] |>
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   465
        eta_contract (member op = cs' orf is_pred pred_arities))) intros;
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   466
    val cnames_syn' = map (fn (s, _) => (s ^ "p", NoSyn)) cnames_syn;
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   467
    val monos' = map (to_pred [] (Context.Proof ctxt)) monos;
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   468
    val ({preds, intrs, elims, raw_induct, ...}, ctxt1) =
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   469
      InductivePackage.add_ind_def verbose "" coind
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   470
        no_elim no_ind cs' intros' monos' params1 cnames_syn' ctxt;
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   471
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   472
    (* define inductive sets using previously defined predicates *)
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   473
    val (defs, ctxt2) = LocalTheory.defs Thm.internalK
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      (map (fn ((c_syn, (fs, U, _)), p) => (c_syn, (("", []),
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   475
         fold_rev lambda params (HOLogic.Collect_const U $
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           HOLogic.ap_split' fs U HOLogic.boolT (list_comb (p, params3))))))
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   477
         (cnames_syn ~~ cs_info ~~ preds)) ctxt1;
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   478
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   479
    (* prove theorems for converting predicate to set notation *)
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   480
    val ctxt3 = fold
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   481
      (fn (((p, c as Free (s, _)), (fs, U, Ts)), (_, (_, def))) => fn ctxt =>
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   482
        let val conv_thm =
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   483
          Goal.prove ctxt (map (fst o dest_Free) params) []
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   484
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
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   485
              (list_comb (p, params3),
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   486
               list_abs (map (pair "x") Ts, HOLogic.mk_mem
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   487
                 (HOLogic.mk_tuple' fs U (map Bound (length fs downto 0)),
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   488
                  list_comb (c, params))))))
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   489
            (K (REPEAT (rtac ext 1) THEN simp_tac (HOL_basic_ss addsimps
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   490
              [def, mem_Collect_eq, split_conv]) 1))
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   491
        in
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   492
          ctxt |> note_theorem ((s ^ "p_" ^ s ^ "_eq",
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   493
            [Attrib.internal (K pred_set_conv_att)]),
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   494
              [conv_thm]) |> snd
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   495
        end) (preds ~~ cs ~~ cs_info ~~ defs) ctxt2;
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   496
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   497
    (* convert theorems to set notation *)
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   498
    val rec_name = if alt_name = "" then
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   499
      space_implode "_" (map fst cnames_syn) else alt_name;
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   500
    val cnames = map (Sign.full_name (ProofContext.theory_of ctxt3) o #1) cnames_syn;  (* FIXME *)
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   501
    val (intr_names, intr_atts) = split_list (map fst intros);
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   502
    val raw_induct' = to_set [] (Context.Proof ctxt3) raw_induct;
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   503
    val (intrs', elims', induct, ctxt4) =
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   504
      InductivePackage.declare_rules rec_name coind no_ind cnames
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   505
      (map (to_set [] (Context.Proof ctxt3)) intrs) intr_names intr_atts
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   506
      (map (fn th => (to_set [] (Context.Proof ctxt3) th,
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   507
         map fst (fst (RuleCases.get th)))) elims)
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   508
      raw_induct' ctxt3
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   509
  in
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   510
    ({intrs = intrs', elims = elims', induct = induct,
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   511
      raw_induct = raw_induct', preds = map fst defs},
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   512
     ctxt4)
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   513
  end;
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   514
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val add_inductive_i = InductivePackage.gen_add_inductive_i add_ind_set_def;
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   516
val add_inductive = InductivePackage.gen_add_inductive add_ind_set_def;
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   517
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   518
val mono_add_att = to_pred_att [] #> InductivePackage.mono_add;
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   519
val mono_del_att = to_pred_att [] #> InductivePackage.mono_del;
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   520
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   521
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   522
(** package setup **)
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   523
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   524
(* setup theory *)
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   525
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   526
val setup =
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   527
  Attrib.add_attributes
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   528
    [("pred_set_conv", Attrib.no_args pred_set_conv_att,
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   529
      "declare rules for converting between predicate and set notation"),
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   530
     ("to_set", Attrib.syntax (Attrib.thms >> to_set_att),
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   531
      "convert rule to set notation"),
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   532
     ("to_pred", Attrib.syntax (Attrib.thms >> to_pred_att),
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   533
      "convert rule to predicate notation")] #>
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   534
  Codegen.add_attribute "ind_set"
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   535
    (Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) >> code_ind_att) #>
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   536
  Codegen.add_preprocessor codegen_preproc #>
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   537
  Attrib.add_attributes [("mono_set", Attrib.add_del_args mono_add_att mono_del_att,
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   538
    "declaration of monotonicity rule for set operators")] #>
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   539
  Context.theory_map (Simplifier.map_ss (fn ss =>
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   540
    ss addsimprocs [collect_mem_simproc]));
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   541
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   542
(* outer syntax *)
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   543
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   544
local structure P = OuterParse and K = OuterKeyword in
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   545
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   546
val ind_set_decl = InductivePackage.gen_ind_decl add_ind_set_def;
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   547
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   548
val inductive_setP =
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   549
  OuterSyntax.command "inductive_set" "define inductive sets" K.thy_decl (ind_set_decl false);
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   550
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   551
val coinductive_setP =
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   552
  OuterSyntax.command "coinductive_set" "define coinductive sets" K.thy_decl (ind_set_decl true);
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   553
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   554
val _ = OuterSyntax.add_parsers [inductive_setP, coinductive_setP];
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   555
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   556
end;
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   557
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   558
end;