src/HOL/Nominal/nominal_fresh_fun.ML
author wenzelm
Sat Apr 16 16:15:37 2011 +0200 (2011-04-16)
changeset 42361 23f352990944
parent 41519 0940fff556a6
child 42364 8c674b3b8e44
permissions -rw-r--r--
modernized structure Proof_Context;
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(*  Title:      HOL/Nominal/nominal_fresh_fun.ML
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    Authors:    Stefan Berghofer and Julien Narboux, TU Muenchen
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Provides a tactic to generate fresh names and
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a tactic to analyse instances of the fresh_fun.
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*)
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(* First some functions that should be in the library *)
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fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
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  let
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    val thy = theory_of_thm st;
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    val cgoal = nth (cprems_of st) (i - 1);
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    val {maxidx, ...} = rep_cterm cgoal;
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    val j = maxidx + 1;
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    val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
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    val ps = Logic.strip_params (term_of cgoal);
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    val Ts = map snd ps;
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    val tinst' = map (fn (t, u) =>
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      (head_of (Logic.incr_indexes (Ts, j) t),
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       list_abs (ps, u))) tinst;
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    val th' = instf
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      (map (pairself (ctyp_of thy)) tyinst')
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      (map (pairself (cterm_of thy)) tinst')
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      (Thm.lift_rule cgoal th)
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  in
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    compose_tac (elim, th', nprems_of th) i st
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  end handle Subscript => Seq.empty;
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val res_inst_tac_term =
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  gen_res_inst_tac_term (curry Thm.instantiate);
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val res_inst_tac_term' =
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  gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
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fun cut_inst_tac_term' tinst th =
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  res_inst_tac_term' tinst false (RuleInsts.make_elim_preserve th);
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fun get_dyn_thm thy name atom_name =
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  Global_Theory.get_thm thy name handle ERROR _ =>
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    error ("The atom type "^atom_name^" is not defined.");
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(* End of function waiting to be in the library :o) *)
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(* The theorems needed that are known at compile time. *)
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val at_exists_fresh' = @{thm "at_exists_fresh'"};
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val fresh_fun_app'   = @{thm "fresh_fun_app'"};
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val fresh_prod       = @{thm "fresh_prod"};
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(* A tactic to generate a name fresh for  all the free *)
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(* variables and parameters of the goal                *)
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fun generate_fresh_tac atom_name i thm =
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 let
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   val thy = theory_of_thm thm;
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(* the parsing function returns a qualified name, we get back the base name *)
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   val atom_basename = Long_Name.base_name atom_name;
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   val goal = List.nth(prems_of thm, i-1);
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   val ps = Logic.strip_params goal;
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   val Ts = rev (map snd ps);
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   fun is_of_fs_name T = Sign.of_sort thy (T, [Sign.intern_class thy ("fs_"^atom_basename)]);
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(* rebuild de bruijn indices *)
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   val bvs = map_index (Bound o fst) ps;
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(* select variables of the right class *)
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   val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
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     (OldTerm.term_frees goal @ bvs);
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(* build the tuple *)
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   val s = (Library.foldr1 (fn (v, s) =>
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       HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs)
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     handle TERM _ => HOLogic.unit;
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   val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
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   val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
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   val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
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(* find the variable we want to instantiate *)
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   val x = hd (OldTerm.term_vars (prop_of exists_fresh'));
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 in
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   (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
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   rtac fs_name_thm 1 THEN
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   etac exE 1) thm
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  handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
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  end;
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fun get_inner_fresh_fun (Bound j) = NONE
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  | get_inner_fresh_fun (v as Free _) = NONE
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  | get_inner_fresh_fun (v as Var _)  = NONE
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  | get_inner_fresh_fun (Const _) = NONE
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  | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t
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  | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u)
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                           = SOME T
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  | get_inner_fresh_fun (t $ u) =
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     let val a = get_inner_fresh_fun u in
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     if a = NONE then get_inner_fresh_fun t else a
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     end;
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(* This tactic generates a fresh name of the atom type *)
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(* given by the innermost fresh_fun                    *)
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fun generate_fresh_fun_tac i thm =
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  let
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    val goal = List.nth(prems_of thm, i-1);
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    val atom_name_opt = get_inner_fresh_fun goal;
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  in
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  case atom_name_opt of
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    NONE => all_tac thm
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  | SOME atom_name  => generate_fresh_tac atom_name i thm
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  end
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(* Two substitution tactics which looks for the innermost occurence in
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   one assumption or in the conclusion *)
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val search_fun = curry (Seq.flat o uncurry EqSubst.searchf_bt_unify_valid);
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val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
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fun subst_inner_tac ctxt = EqSubst.eqsubst_tac' ctxt search_fun;
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fun subst_inner_asm_tac_aux i ctxt = EqSubst.eqsubst_asm_tac' ctxt search_fun_asm i;
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(* A tactic to substitute in the first assumption
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   which contains an occurence. *)
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fun subst_inner_asm_tac ctxt th =
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  curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux
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            (1 upto Thm.nprems_of th)))))) ctxt th;
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fun fresh_fun_tac no_asm i thm =
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  (* Find the variable we instantiate *)
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  let
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    val thy = theory_of_thm thm;
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    val ctxt = Proof_Context.init_global thy;
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    val ss = global_simpset_of thy;
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    val abs_fresh = Global_Theory.get_thms thy "abs_fresh";
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    val fresh_perm_app = Global_Theory.get_thms thy "fresh_perm_app";
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    val ss' = ss addsimps fresh_prod::abs_fresh;
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    val ss'' = ss' addsimps fresh_perm_app;
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    val x = hd (tl (OldTerm.term_vars (prop_of exI)));
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    val goal = nth (prems_of thm) (i-1);
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    val atom_name_opt = get_inner_fresh_fun goal;
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    val n = length (Logic.strip_params goal);
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    (* Here we rely on the fact that the variable introduced by generate_fresh_tac *)
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    (* is the last one in the list, the inner one *)
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  in
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  case atom_name_opt of
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    NONE => all_tac thm
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  | SOME atom_name =>
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  let
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    val atom_basename = Long_Name.base_name atom_name;
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    val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
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    val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
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    fun inst_fresh vars params i st =
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   let val vars' = OldTerm.term_vars (prop_of st);
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       val thy = theory_of_thm st;
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   in case subtract (op =) vars vars' of
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     [x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st)
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    | _ => error "fresh_fun_simp: Too many variables, please report."
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  end
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  in
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  ((fn st =>
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  let
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    val vars = OldTerm.term_vars (prop_of st);
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    val params = Logic.strip_params (nth (prems_of st) (i-1))
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    (* The tactics which solve the subgoals generated
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       by the conditionnal rewrite rule. *)
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    val post_rewrite_tacs =
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          [rtac pt_name_inst,
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           rtac at_name_inst,
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           TRY o SOLVED' (NominalPermeq.finite_guess_tac ss''),
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           inst_fresh vars params THEN'
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           (TRY o SOLVED' (NominalPermeq.fresh_guess_tac ss'')) THEN'
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           (TRY o SOLVED' (asm_full_simp_tac ss''))]
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  in
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   ((if no_asm then no_tac else
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    (subst_inner_asm_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i)))
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    ORELSE
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    (subst_inner_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i))) st
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  end)) thm
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  end
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  end
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(* syntax for options, given "(no_asm)" will give back true, without
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   gives back false *)
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val options_syntax =
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    (Args.parens (Args.$$$ "no_asm") >> (K true)) ||
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     (Scan.succeed false);
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fun setup_generate_fresh x =
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  (Args.goal_spec -- Args.type_name true >>
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    (fn (quant, s) => K (SIMPLE_METHOD'' quant (generate_fresh_tac s)))) x;
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fun setup_fresh_fun_simp x =
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  (Scan.lift options_syntax >> (fn b => K (SIMPLE_METHOD' (fresh_fun_tac b)))) x;
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