src/HOL/Tools/recdef_package.ML
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(*  Title:      HOL/Tools/recdef_package.ML
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    Author:     Markus Wenzel, TU Muenchen
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Wrapper module for Konrad Slind's TFL package.
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*)
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signature RECDEF_PACKAGE =
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sig
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  val get_recdef: theory -> string
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    -> {simps: thm list, rules: thm list list, induct: thm, tcs: term list} option
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  val get_hints: Proof.context -> {simps: thm list, congs: (string * thm) list, wfs: thm list}
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  val simp_add: attribute
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  val simp_del: attribute
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  val cong_add: attribute
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  val cong_del: attribute
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  val wf_add: attribute
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  val wf_del: attribute
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  val add_recdef: bool -> xstring -> string -> ((binding * string) * Attrib.src list) list ->
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    Attrib.src option -> theory -> theory
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      * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
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  val add_recdef_i: bool -> xstring -> term -> ((binding * term) * attribute list) list ->
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    theory -> theory * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
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  val defer_recdef: xstring -> string list -> (Facts.ref * Attrib.src list) list
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    -> theory -> theory * {induct_rules: thm}
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  val defer_recdef_i: xstring -> term list -> thm list -> theory -> theory * {induct_rules: thm}
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  val recdef_tc: bstring * Attrib.src list -> xstring -> int option -> bool ->
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    local_theory -> Proof.state
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  val recdef_tc_i: bstring * Attrib.src list -> string -> int option -> bool ->
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    local_theory -> Proof.state
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  val setup: theory -> theory
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end;
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structure RecdefPackage: RECDEF_PACKAGE =
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struct
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(** recdef hints **)
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(* type hints *)
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type hints = {simps: thm list, congs: (string * thm) list, wfs: thm list};
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fun mk_hints (simps, congs, wfs) = {simps = simps, congs = congs, wfs = wfs}: hints;
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fun map_hints f ({simps, congs, wfs}: hints) = mk_hints (f (simps, congs, wfs));
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fun map_simps f = map_hints (fn (simps, congs, wfs) => (f simps, congs, wfs));
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fun map_congs f = map_hints (fn (simps, congs, wfs) => (simps, f congs, wfs));
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fun map_wfs f = map_hints (fn (simps, congs, wfs) => (simps, congs, f wfs));
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fun pretty_hints ({simps, congs, wfs}: hints) =
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 [Pretty.big_list "recdef simp hints:" (map Display.pretty_thm simps),
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  Pretty.big_list "recdef cong hints:" (map Display.pretty_thm (map snd congs)),
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  Pretty.big_list "recdef wf hints:" (map Display.pretty_thm wfs)];
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(* congruence rules *)
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local
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val cong_head =
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  fst o Term.dest_Const o Term.head_of o fst o Logic.dest_equals o Thm.concl_of;
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fun prep_cong raw_thm =
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  let val thm = safe_mk_meta_eq raw_thm in (cong_head thm, thm) end;
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in
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fun add_cong raw_thm congs =
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  let
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    val (c, thm) = prep_cong raw_thm;
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    val _ = if AList.defined (op =) congs c
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      then warning ("Overwriting recdef congruence rule for " ^ quote c)
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      else ();
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  in AList.update (op =) (c, thm) congs end;
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fun del_cong raw_thm congs =
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  let
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    val (c, thm) = prep_cong raw_thm;
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    val _ = if AList.defined (op =) congs c
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      then ()
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      else warning ("No recdef congruence rule for " ^ quote c);
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  in AList.delete (op =) c congs end;
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end;
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(** global and local recdef data **)
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(* theory data *)
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type recdef_info = {simps: thm list, rules: thm list list, induct: thm, tcs: term list};
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structure GlobalRecdefData = TheoryDataFun
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(
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  type T = recdef_info Symtab.table * hints;
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  val empty = (Symtab.empty, mk_hints ([], [], [])): T;
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  val copy = I;
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  val extend = I;
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  fun merge _
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   ((tab1, {simps = simps1, congs = congs1, wfs = wfs1}),
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    (tab2, {simps = simps2, congs = congs2, wfs = wfs2})) : T =
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      (Symtab.merge (K true) (tab1, tab2),
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        mk_hints (Thm.merge_thms (simps1, simps2),
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          AList.merge (op =) Thm.eq_thm (congs1, congs2),
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          Thm.merge_thms (wfs1, wfs2)));
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);
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val get_recdef = Symtab.lookup o #1 o GlobalRecdefData.get;
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fun put_recdef name info thy =
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  let
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    val (tab, hints) = GlobalRecdefData.get thy;
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    val tab' = Symtab.update_new (name, info) tab
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      handle Symtab.DUP _ => error ("Duplicate recursive function definition " ^ quote name);
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  in GlobalRecdefData.put (tab', hints) thy end;
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val get_global_hints = #2 o GlobalRecdefData.get;
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(* proof data *)
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structure LocalRecdefData = ProofDataFun
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(
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  type T = hints;
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  val init = get_global_hints;
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);
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val get_hints = LocalRecdefData.get;
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fun map_hints f = Context.mapping (GlobalRecdefData.map (apsnd f)) (LocalRecdefData.map f);
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(* attributes *)
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fun attrib f = Thm.declaration_attribute (map_hints o f);
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val simp_add = attrib (map_simps o Thm.add_thm);
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val simp_del = attrib (map_simps o Thm.del_thm);
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val cong_add = attrib (map_congs o add_cong);
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val cong_del = attrib (map_congs o del_cong);
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val wf_add = attrib (map_wfs o Thm.add_thm);
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val wf_del = attrib (map_wfs o Thm.del_thm);
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(* modifiers *)
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val recdef_simpN = "recdef_simp";
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val recdef_congN = "recdef_cong";
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val recdef_wfN = "recdef_wf";
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val recdef_modifiers =
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 [Args.$$$ recdef_simpN -- Args.colon >> K ((I, simp_add): Method.modifier),
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  Args.$$$ recdef_simpN -- Args.add -- Args.colon >> K (I, simp_add),
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  Args.$$$ recdef_simpN -- Args.del -- Args.colon >> K (I, simp_del),
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  Args.$$$ recdef_congN -- Args.colon >> K (I, cong_add),
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  Args.$$$ recdef_congN -- Args.add -- Args.colon >> K (I, cong_add),
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  Args.$$$ recdef_congN -- Args.del -- Args.colon >> K (I, cong_del),
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  Args.$$$ recdef_wfN -- Args.colon >> K (I, wf_add),
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  Args.$$$ recdef_wfN -- Args.add -- Args.colon >> K (I, wf_add),
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  Args.$$$ recdef_wfN -- Args.del -- Args.colon >> K (I, wf_del)] @
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  Clasimp.clasimp_modifiers;
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(** prepare_hints(_i) **)
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fun prepare_hints thy opt_src =
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  let
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    val ctxt0 = ProofContext.init thy;
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    val ctxt =
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      (case opt_src of
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        NONE => ctxt0
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      | SOME src => Method.only_sectioned_args recdef_modifiers I src ctxt0);
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    val {simps, congs, wfs} = get_hints ctxt;
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    val cs = local_claset_of ctxt;
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    val ss = local_simpset_of ctxt addsimps simps;
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  in (cs, ss, rev (map snd congs), wfs) end;
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fun prepare_hints_i thy () =
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  let
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    val ctxt0 = ProofContext.init thy;
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    val {simps, congs, wfs} = get_global_hints thy;
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  in (local_claset_of ctxt0, local_simpset_of ctxt0 addsimps simps, rev (map snd congs), wfs) end;
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(** add_recdef(_i) **)
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fun requires_recdef thy = Theory.requires thy "Recdef" "recursive functions";
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fun gen_add_recdef tfl_fn prep_att prep_hints not_permissive raw_name R eq_srcs hints thy =
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  let
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    val _ = requires_recdef thy;
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    val name = Sign.intern_const thy raw_name;
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    val bname = Sign.base_name name;
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    val _ = writeln ("Defining recursive function " ^ quote name ^ " ...");
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    val ((eq_names, eqs), raw_eq_atts) = apfst split_list (split_list eq_srcs);
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    val eq_atts = map (map (prep_att thy)) raw_eq_atts;
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    val (cs, ss, congs, wfs) = prep_hints thy hints;
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    (*We must remove imp_cong to prevent looping when the induction rule
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      is simplified. Many induction rules have nested implications that would
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      give rise to looping conditional rewriting.*)
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    val (thy, {rules = rules_idx, induct, tcs}) =
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        tfl_fn not_permissive thy cs (ss delcongs [imp_cong])
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               congs wfs name R eqs;
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    val rules = (map o map) fst (partition_eq (eq_snd (op = : int * int -> bool)) rules_idx);
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    val simp_att = if null tcs then [Simplifier.simp_add, Nitpick_Const_Simp_Thms.add,
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      Code.add_default_eqn_attribute] else [];
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    val ((simps' :: rules', [induct']), thy) =
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      thy
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      |> Sign.add_path bname
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      |> PureThy.add_thmss
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        (((Binding.name "simps", List.concat rules), simp_att) :: ((eq_names ~~ rules) ~~ eq_atts))
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      ||>> PureThy.add_thms [((Binding.name "induct", induct), [])];
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    val result = {simps = simps', rules = rules', induct = induct', tcs = tcs};
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    val thy =
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      thy
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      |> put_recdef name result
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      |> Sign.parent_path;
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  in (thy, result) end;
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val add_recdef = gen_add_recdef Tfl.define Attrib.attribute prepare_hints;
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fun add_recdef_i x y z w = gen_add_recdef Tfl.define_i (K I) prepare_hints_i x y z w ();
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(** defer_recdef(_i) **)
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fun gen_defer_recdef tfl_fn eval_thms raw_name eqs raw_congs thy =
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  let
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    val name = Sign.intern_const thy raw_name;
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    val bname = Sign.base_name name;
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    val _ = requires_recdef thy;
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    val _ = writeln ("Deferred recursive function " ^ quote name ^ " ...");
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    val congs = eval_thms (ProofContext.init thy) raw_congs;
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    val (thy2, induct_rules) = tfl_fn thy congs name eqs;
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    val ([induct_rules'], thy3) =
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      thy2
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      |> Sign.add_path bname
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      |> PureThy.add_thms [((Binding.name "induct_rules", induct_rules), [])]
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      ||> Sign.parent_path;
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  in (thy3, {induct_rules = induct_rules'}) end;
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val defer_recdef = gen_defer_recdef Tfl.defer Attrib.eval_thms;
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val defer_recdef_i = gen_defer_recdef Tfl.defer_i (K I);
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d7e7532c128a peoper defer_recdef interface;
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(** recdef_tc(_i) **)
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fun gen_recdef_tc prep_att prep_name (bname, raw_atts) raw_name opt_i int lthy =
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  let
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    val thy = ProofContext.theory_of lthy;
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    val name = prep_name thy raw_name;
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    val atts = map (prep_att thy) raw_atts;
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    val tcs =
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      (case get_recdef thy name of
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        NONE => error ("No recdef definition of constant: " ^ quote name)
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      | SOME {tcs, ...} => tcs);
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    val i = the_default 1 opt_i;
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    val tc = nth tcs (i - 1) handle Subscript =>
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      error ("No termination condition #" ^ string_of_int i ^
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        " in recdef definition of " ^ quote name);
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  in
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    Specification.theorem Thm.internalK NONE (K I) (Binding.name bname, atts)
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      [] (Element.Shows [(Attrib.empty_binding, [(HOLogic.mk_Trueprop tc, [])])]) int lthy
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  end;
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val recdef_tc = gen_recdef_tc Attrib.intern_src Sign.intern_const;
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val recdef_tc_i = gen_recdef_tc (K I) (K I);
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(** package setup **)
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(* setup theory *)
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val setup =
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  Attrib.add_attributes
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   [(recdef_simpN, Attrib.add_del_args simp_add simp_del, "declaration of recdef simp rule"),
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    (recdef_congN, Attrib.add_del_args cong_add cong_del, "declaration of recdef cong rule"),
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    (recdef_wfN, Attrib.add_del_args wf_add wf_del, "declaration of recdef wf rule")];
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(* outer syntax *)
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local structure P = OuterParse and K = OuterKeyword in
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val _ = List.app OuterKeyword.keyword ["permissive", "congs", "hints"];
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val hints =
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  P.$$$ "(" |-- P.!!! (P.position (P.$$$ "hints" -- Args.parse) --| P.$$$ ")") >> Args.src;
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val recdef_decl =
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  Scan.optional (P.$$$ "(" -- P.!!! (P.$$$ "permissive" -- P.$$$ ")") >> K false) true --
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  P.name -- P.term -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop)
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    -- Scan.option hints
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  >> (fn ((((p, f), R), eqs), src) => #1 o add_recdef p f R (map P.triple_swap eqs) src);
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val _ =
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  OuterSyntax.command "recdef" "define general recursive functions (TFL)" K.thy_decl
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    (recdef_decl >> Toplevel.theory);
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val defer_recdef_decl =
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  P.name -- Scan.repeat1 P.prop --
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  Scan.optional (P.$$$ "(" |-- P.$$$ "congs" |-- P.!!! (SpecParse.xthms1 --| P.$$$ ")")) []
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  >> (fn ((f, eqs), congs) => #1 o defer_recdef f eqs congs);
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val _ =
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  OuterSyntax.command "defer_recdef" "defer general recursive functions (TFL)" K.thy_decl
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    (defer_recdef_decl >> Toplevel.theory);
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val _ =
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  OuterSyntax.local_theory_to_proof' "recdef_tc" "recommence proof of termination condition (TFL)"
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    K.thy_goal
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    ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name) -- P.xname --
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        Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")")
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      >> (fn ((thm_name, name), i) => recdef_tc thm_name name i));
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end;
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end;