src/HOL/Tools/recdef_package.ML
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local_cla/simpset_of;
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(*  Title:      HOL/Tools/recdef_package.ML
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    ID:         $Id$
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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 quiet_mode: bool ref
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  val print_recdefs: theory -> unit
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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 simp_add_global: theory attribute
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  val simp_del_global: theory attribute
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  val cong_add_global: theory attribute
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  val cong_del_global: theory attribute
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  val wf_add_global: theory attribute
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  val wf_del_global: theory attribute
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  val simp_add_local: Proof.context attribute
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  val simp_del_local: Proof.context attribute
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  val cong_add_local: Proof.context attribute
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  val cong_del_local: Proof.context attribute
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  val wf_add_local: Proof.context attribute
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  val wf_del_local: Proof.context attribute
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  val add_recdef: bool -> xstring -> string -> ((bstring * string) * Args.src list) list ->
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    Args.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 -> ((bstring * term) * theory 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 add_recdef_old: xstring -> string -> ((bstring * string) * Args.src list) list ->
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    simpset * thm list -> theory ->
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    theory * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
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  val defer_recdef: xstring -> string list -> (xstring * Args.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 attribute list) list
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    -> theory -> theory * {induct_rules: thm}
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  val recdef_tc: bstring * Args.src list -> xstring -> int option
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    -> bool -> theory -> ProofHistory.T
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  val recdef_tc_i: bstring * theory attribute list -> string -> int option
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    -> bool -> theory -> ProofHistory.T
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  val setup: (theory -> theory) list
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end;
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structure RecdefPackage: RECDEF_PACKAGE =
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struct
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val quiet_mode = Tfl.quiet_mode;
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val message = Tfl.message;
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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 #2 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 val (c, thm) = prep_cong raw_thm
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  in overwrite_warn (congs, (c, thm)) ("Overwriting recdef congruence rule for " ^ quote c) 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 (del, rest) = Library.partition (Library.equal c o fst) congs;
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  in if null del then (warning ("No recdef congruence rule for " ^ quote c); congs) else rest end;
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val add_congs = curry (foldr (uncurry add_cong));
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end;
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(** global and local recdef data **)
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(* theory data kind 'HOL/recdef' *)
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type recdef_info = {simps: thm list, rules: thm list list, induct: thm, tcs: term list};
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structure GlobalRecdefArgs =
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struct
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  val name = "HOL/recdef";
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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 prep_ext = 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})) =
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      (Symtab.merge (K true) (tab1, tab2),
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        mk_hints (Drule.merge_rules (simps1, simps2),
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          Library.merge_alists congs1 congs2,
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          Drule.merge_rules (wfs1, wfs2)));
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  fun print sg (tab, hints) =
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   (Pretty.strs ("recdefs:" :: map #1 (Sign.cond_extern_table sg Sign.constK tab)) ::
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     pretty_hints hints) |> Pretty.chunks |> Pretty.writeln;
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end;
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structure GlobalRecdefData = TheoryDataFun(GlobalRecdefArgs);
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val print_recdefs = GlobalRecdefData.print;
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fun get_recdef thy name = Symtab.lookup (#1 (GlobalRecdefData.get thy), name);
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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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val map_global_hints = GlobalRecdefData.map o apsnd;
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(* proof data kind 'HOL/recdef' *)
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structure LocalRecdefArgs =
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struct
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  val name = "HOL/recdef";
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  type T = hints;
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  val init = get_global_hints;
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  fun print _ hints = pretty_hints hints |> Pretty.chunks |> Pretty.writeln;
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end;
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structure LocalRecdefData = ProofDataFun(LocalRecdefArgs);
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val get_local_hints = LocalRecdefData.get;
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val map_local_hints = LocalRecdefData.map;
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(* attributes *)
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local
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fun global_local f g =
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 (fn (thy, thm) => (map_global_hints (f (g thm)) thy, thm),
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  fn (ctxt, thm) => (map_local_hints (f (g thm)) ctxt, thm));
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fun mk_attr (add1, add2) (del1, del2) =
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 (Attrib.add_del_args add1 del1, Attrib.add_del_args add2 del2);
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in
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val (simp_add_global, simp_add_local) = global_local map_simps Drule.add_rule;
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val (simp_del_global, simp_del_local) = global_local map_simps Drule.del_rule;
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val (cong_add_global, cong_add_local) = global_local map_congs add_cong;
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val (cong_del_global, cong_del_local) = global_local map_congs del_cong;
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val (wf_add_global, wf_add_local) = global_local map_wfs Drule.add_rule;
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val (wf_del_global, wf_del_local) = global_local map_wfs Drule.del_rule;
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val simp_attr = mk_attr (simp_add_global, simp_add_local) (simp_del_global, simp_del_local);
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val cong_attr = mk_attr (cong_add_global, cong_add_local) (cong_del_global, cong_del_local);
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val wf_attr = mk_attr (wf_add_global, wf_add_local) (wf_del_global, wf_del_local);
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end;
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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.$$$ recdef_simpN -- Args.colon >> K ((I, simp_add_local): Method.modifier),
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  Args.$$$ recdef_simpN -- Args.add -- Args.colon >> K (I, simp_add_local),
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  Args.$$$ recdef_simpN -- Args.del -- Args.colon >> K (I, simp_del_local),
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  Args.$$$ recdef_congN -- Args.colon >> K (I, cong_add_local),
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  Args.$$$ recdef_congN -- Args.add -- Args.colon >> K (I, cong_add_local),
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  Args.$$$ recdef_congN -- Args.del -- Args.colon >> K (I, cong_del_local),
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  Args.$$$ recdef_wfN -- Args.colon >> K (I, wf_add_local),
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  Args.$$$ recdef_wfN -- Args.add -- Args.colon >> K (I, wf_add_local),
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  Args.$$$ recdef_wfN -- Args.del -- Args.colon >> K (I, wf_del_local)] @
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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_local_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, map #2 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, map #2 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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(*"strict" is true iff (permissive) has been omitted*)
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fun gen_add_recdef tfl_fn prep_att prep_hints strict 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 (Theory.sign_of thy) raw_name;
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    val bname = Sign.base_name name;
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    val _ = message ("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 strict thy cs (ss delcongs [imp_cong])
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               congs wfs name R eqs;
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    val rules = map (map #1) (Library.partition_eq Library.eq_snd rules_idx);
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    val simp_att = if null tcs then
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      [Simplifier.simp_add_global, RecfunCodegen.add] else [];
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    val (thy, (simps' :: rules', [induct'])) =
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      thy
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      |> Theory.add_path bname
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      |> PureThy.add_thmss ((("simps", flat rules), simp_att) :: ((eq_names ~~ rules) ~~ eq_atts))
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      |>>> PureThy.add_thms [(("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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      |> Theory.parent_path;
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  in (thy, result) end;
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val add_recdef = gen_add_recdef Tfl.define Attrib.global_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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(* add_recdef_old -- legacy interface *)
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fun prepare_hints_old thy (ss, thms) =
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  let val {simps, congs, wfs} = get_global_hints thy
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  in (Classical.claset_of thy, ss addsimps simps, map #2 (add_congs thms congs), wfs) end;
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val add_recdef_old = gen_add_recdef Tfl.define Attrib.global_attribute prepare_hints_old false;
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(** defer_recdef(_i) **)
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fun gen_defer_recdef tfl_fn app_thms raw_name eqs raw_congs thy =
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  let
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    val name = Sign.intern_const (Theory.sign_of 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 _ = message ("Deferred recursive function " ^ quote name ^ " ...");
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    val (thy1, congs) = thy |> app_thms raw_congs;
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    val (thy2, induct_rules) = tfl_fn thy1 congs name eqs;
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    val (thy3, [induct_rules']) =
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      thy2
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      |> Theory.add_path bname
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      |> PureThy.add_thms [(("induct_rules", induct_rules), [])]
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      |>> Theory.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 IsarThy.apply_theorems;
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val defer_recdef_i = gen_defer_recdef Tfl.defer_i IsarThy.apply_theorems_i;
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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 thy =
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  let
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    val name = prep_name (Theory.sign_of 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 = if_none opt_i 1;
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    val tc = Library.nth_elem (i - 1, tcs) handle Library.LIST _ =>
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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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    thy
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    |> IsarThy.theorem_i Drule.internalK ((bname, atts), (HOLogic.mk_Trueprop tc, ([], []))) int
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  end;
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val recdef_tc = gen_recdef_tc Attrib.global_attribute 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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 [GlobalRecdefData.init, LocalRecdefData.init,
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  Attrib.add_attributes
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   [(recdef_simpN, simp_attr, "declaration of recdef simp rule"),
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    (recdef_congN, cong_attr, "declaration of recdef cong rule"),
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    (recdef_wfN, wf_attr, "declaration of recdef wf rule")]];
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7eea9f25dc49 'HOL/recdef' theory data;
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(* outer syntax *)
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local structure P = OuterParse and K = OuterSyntax.Keyword in
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val hints =
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  P.$$$ "(" |-- P.!!! (P.position (P.$$$ "hints" -- P.arguments) --| P.$$$ ")") >> Args.src;
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val recdef_decl =
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  Scan.optional (P.$$$ "(" -- P.!!! (P.$$$ "permissive" -- P.$$$ ")") >> K false) true --
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  P.name -- P.term -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop) -- Scan.option hints
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  >> (fn ((((p, f), R), eqs), src) => #1 o add_recdef p f R (map P.triple_swap eqs) src);
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val recdefP =
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  OuterSyntax.command "recdef" "define general recursive functions (TFL)" K.thy_decl
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    (recdef_decl >> Toplevel.theory);
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val defer_recdef_decl =
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  P.name -- Scan.repeat1 P.prop --
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  Scan.optional (P.$$$ "(" |-- P.$$$ "congs" |-- P.!!! (P.xthms1 --| P.$$$ ")")) []
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  >> (fn ((f, eqs), congs) => #1 o defer_recdef f eqs congs);
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val defer_recdefP =
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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 recdef_tc_decl =
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  P.opt_thm_name ":" -- P.xname -- Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")");
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fun mk_recdef_tc ((thm_name, name), i) = recdef_tc thm_name name i;
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val recdef_tcP =
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  OuterSyntax.command "recdef_tc" "recommence proof of termination condition (TFL)" K.thy_goal
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    (recdef_tc_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_recdef_tc)));
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val _ = OuterSyntax.add_keywords ["permissive", "congs", "hints"];
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val _ = OuterSyntax.add_parsers [recdefP, defer_recdefP, recdef_tcP];
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end;
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end;