# File recdef_package.ML

    (*  Title:      HOL/Tools/recdef_package.ML
        ID:         $Id: recdef_package.ML,v 1.62 2005/09/23 07:00:19 haftmann Exp $
        Author:     Markus Wenzel, TU Muenchen

    Wrapper module for Konrad Slind's TFL package.
    *)

    signature RECDEF_PACKAGE =
    sig
      val quiet_mode: bool ref
      val print_recdefs: theory -> unit
      val get_recdef: theory -> string
        -> {simps: thm list, rules: thm list list, induct: thm, tcs: term list} option
      val simp_add_global: theory attribute
      val simp_del_global: theory attribute
      val cong_add_global: theory attribute
      val cong_del_global: theory attribute
      val wf_add_global: theory attribute
      val wf_del_global: theory attribute
      val simp_add_local: Proof.context attribute
      val simp_del_local: Proof.context attribute
      val cong_add_local: Proof.context attribute
      val cong_del_local: Proof.context attribute
      val wf_add_local: Proof.context attribute
      val wf_del_local: Proof.context attribute
      val add_recdef: bool -> xstring -> string -> ((bstring * string) * Attrib.src list) list ->
        Attrib.src option -> theory -> theory
          * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
      val add_recdef_i: bool -> xstring -> term -> ((bstring * term) * theory attribute list) list ->
        theory -> theory * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
      val add_recdef_old: xstring -> string -> ((bstring * string) * Attrib.src list) list ->
        simpset * thm list -> theory ->
        theory * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
      val defer_recdef: xstring -> string list -> (thmref * Attrib.src list) list
        -> theory -> theory * {induct_rules: thm}
      val defer_recdef_i: xstring -> term list -> (thm list * theory attribute list) list
        -> theory -> theory * {induct_rules: thm}
      val recdef_tc: bstring * Attrib.src list -> xstring -> int option -> theory -> Proof.state
      val recdef_tc_i: bstring * theory attribute list -> string -> int option
        -> theory -> Proof.state
      val setup: (theory -> theory) list
    end;

    structure RecdefPackage: RECDEF_PACKAGE =
    struct

    val quiet_mode = Tfl.quiet_mode;
    val message = Tfl.message;

    (** recdef hints **)

    (* type hints *)

    type hints = {simps: thm list, congs: (string * thm) list, wfs: thm list};

    fun mk_hints (simps, congs, wfs) = {simps = simps, congs = congs, wfs = wfs}: hints;
    fun map_hints f ({simps, congs, wfs}: hints) = mk_hints (f (simps, congs, wfs));

    fun map_simps f = map_hints (fn (simps, congs, wfs) => (f simps, congs, wfs));
    fun map_congs f = map_hints (fn (simps, congs, wfs) => (simps, f congs, wfs));
    fun map_wfs f = map_hints (fn (simps, congs, wfs) => (simps, congs, f wfs));

    fun pretty_hints ({simps, congs, wfs}: hints) =
     [Pretty.big_list "recdef simp hints:" (map Display.pretty_thm simps),
      Pretty.big_list "recdef cong hints:" (map Display.pretty_thm (map #2 congs)),
      Pretty.big_list "recdef wf hints:" (map Display.pretty_thm wfs)];

    (* congruence rules *)

    local

    val cong_head =
      fst o Term.dest_Const o Term.head_of o fst o Logic.dest_equals o Thm.concl_of;

    fun prep_cong raw_thm =
      let val thm = safe_mk_meta_eq raw_thm in (cong_head thm, thm) end;

    in

    fun add_cong raw_thm congs =
      let val (c, thm) = prep_cong raw_thm
    (*   in update_warn (op =) ("Overwriting recdef congruence rule for " ^ quote c) (c, thm) congs end;  *)
      in overwrite_warn (congs, (c, thm)) ("Overwriting recdef congruence rule for " ^ quote c) end;

    fun del_cong raw_thm congs =
      let
        val (c, thm) = prep_cong raw_thm;
        val (del, rest) = Library.partition (Library.equal c o fst) congs;
      in if null del then (warning ("No recdef congruence rule for " ^ quote c); congs) else rest end;

    val add_congs = foldr (uncurry add_cong);

    end;

    (** global and local recdef data **)

    (* theory data kind 'HOL/recdef' *)

    type recdef_info = {simps: thm list, rules: thm list list, induct: thm, tcs: term list};

    structure GlobalRecdefData = TheoryDataFun
    (struct
      val name = "HOL/recdef";
      type T = recdef_info Symtab.table * hints;

      val empty = (Symtab.empty, mk_hints ([], [], [])): T;
      val copy = I;
      val extend = I;
      fun merge _
       ((tab1, {simps = simps1, congs = congs1, wfs = wfs1}),
        (tab2, {simps = simps2, congs = congs2, wfs = wfs2})) : T =
          (Symtab.merge (K true) (tab1, tab2),
            mk_hints (Drule.merge_rules (simps1, simps2),
              Library.merge_alists congs1 congs2,
              Drule.merge_rules (wfs1, wfs2)));

      fun print thy (tab, hints) =
        (Pretty.strs ("recdefs:" :: map #1 (NameSpace.extern_table (Sign.const_space thy, tab))) ::
          pretty_hints hints) |> Pretty.chunks |> Pretty.writeln;
    end);

    val print_recdefs = GlobalRecdefData.print;

    val get_recdef = Symtab.lookup o #1 o GlobalRecdefData.get;

    fun put_recdef name info thy =
      let
        val (tab, hints) = GlobalRecdefData.get thy;
        val tab' = Symtab.update_new (name, info) tab
          handle Symtab.DUP _ => error ("Duplicate recursive function definition " ^ quote name);
      in GlobalRecdefData.put (tab', hints) thy end;

    val get_global_hints = #2 o GlobalRecdefData.get;
    val map_global_hints = GlobalRecdefData.map o apsnd;

    (* proof data kind 'HOL/recdef' *)

    structure LocalRecdefData = ProofDataFun
    (struct
      val name = "HOL/recdef";
      type T = hints;
      val init = get_global_hints;
      fun print _ hints = pretty_hints hints |> Pretty.chunks |> Pretty.writeln;
    end);

    val get_local_hints = LocalRecdefData.get;
    val map_local_hints = LocalRecdefData.map;

    (* attributes *)

    local

    fun global_local f g =
     (fn (thy, thm) => (map_global_hints (f (g thm)) thy, thm),
      fn (ctxt, thm) => (map_local_hints (f (g thm)) ctxt, thm));

    fun mk_attr (add1, add2) (del1, del2) =
     (Attrib.add_del_args add1 del1, Attrib.add_del_args add2 del2);

    in

    val (simp_add_global, simp_add_local) = global_local map_simps Drule.add_rule;
    val (simp_del_global, simp_del_local) = global_local map_simps Drule.del_rule;
    val (cong_add_global, cong_add_local) = global_local map_congs add_cong;
    val (cong_del_global, cong_del_local) = global_local map_congs del_cong;
    val (wf_add_global, wf_add_local) = global_local map_wfs Drule.add_rule;
    val (wf_del_global, wf_del_local) = global_local map_wfs Drule.del_rule;

    val simp_attr = mk_attr (simp_add_global, simp_add_local) (simp_del_global, simp_del_local);
    val cong_attr = mk_attr (cong_add_global, cong_add_local) (cong_del_global, cong_del_local);
    val wf_attr = mk_attr (wf_add_global, wf_add_local) (wf_del_global, wf_del_local);

    end;

    (* modifiers *)

    val recdef_simpN = "recdef_simp";
    val recdef_congN = "recdef_cong";
    val recdef_wfN = "recdef_wf";

    val recdef_modifiers =
     [Args.$$$ recdef_simpN -- Args.colon >> K ((I, simp_add_local): Method.modifier),
      Args.$$$ recdef_simpN -- Args.add -- Args.colon >> K (I, simp_add_local),
      Args.$$$ recdef_simpN -- Args.del -- Args.colon >> K (I, simp_del_local),
      Args.$$$ recdef_congN -- Args.colon >> K (I, cong_add_local),
      Args.$$$ recdef_congN -- Args.add -- Args.colon >> K (I, cong_add_local),
      Args.$$$ recdef_congN -- Args.del -- Args.colon >> K (I, cong_del_local),
      Args.$$$ recdef_wfN -- Args.colon >> K (I, wf_add_local),
      Args.$$$ recdef_wfN -- Args.add -- Args.colon >> K (I, wf_add_local),
      Args.$$$ recdef_wfN -- Args.del -- Args.colon >> K (I, wf_del_local)] @
      Clasimp.clasimp_modifiers;

    (** prepare_hints(_i) **)

    fun prepare_hints thy opt_src =
      let
        val ctxt0 = ProofContext.init thy;
        val ctxt =
          (case opt_src of
            NONE => ctxt0
          | SOME src => Method.only_sectioned_args recdef_modifiers I src ctxt0);
        val {simps, congs, wfs} = get_local_hints ctxt;
        val cs = local_claset_of ctxt;
        val ss = local_simpset_of ctxt addsimps simps;
      in (cs, ss, map #2 congs, wfs) end;

    fun prepare_hints_i thy () =
      let
        val ctxt0 = ProofContext.init thy;
        val {simps, congs, wfs} = get_global_hints thy;
      in (local_claset_of ctxt0, local_simpset_of ctxt0 addsimps simps, map #2 congs, wfs) end;

    (** add_recdef(_i) **)

    fun requires_recdef thy = Theory.requires thy "Recdef" "recursive functions";

    (*"strict" is true iff (permissive) has been omitted*)
    fun gen_add_recdef tfl_fn prep_att prep_hints strict raw_name R eq_srcs hints thy =
      let
        val _ = requires_recdef thy;

        val name = Sign.intern_const thy raw_name;
        val bname = Sign.base_name name;
        val _ = message ("Defining recursive function " ^ quote name ^ " ...");

        val ((eq_names, eqs), raw_eq_atts) = apfst split_list (split_list eq_srcs);
        val eq_atts = map (map (prep_att thy)) raw_eq_atts;

        val (cs, ss, congs, wfs) = prep_hints thy hints;
        (*We must remove imp_cong to prevent looping when the induction rule
          is simplified. Many induction rules have nested implications that would
          give rise to looping conditional rewriting.*)
        val (thy, {rules = rules_idx, induct, tcs}) =
            tfl_fn strict thy cs (ss delcongs [imp_cong])
                   congs wfs name R eqs;
        val rules = map (map #1) (Library.partition_eq (Library.eq_snd (op =)) rules_idx);
        val simp_att = if null tcs then
          [Simplifier.simp_add_global, RecfunCodegen.add NONE] else [];

        val (thy, (simps' :: rules', [induct'])) =
          thy
          |> Theory.add_path bname
          |> PureThy.add_thmss ((("simps", List.concat rules), simp_att) :: ((eq_names ~~ rules) ~~ eq_atts))
          |>>> PureThy.add_thms [(("induct", induct), [])];
        val result = {simps = simps', rules = rules', induct = induct', tcs = tcs};
        val thy =
          thy
          |> put_recdef name result
          |> Theory.parent_path;
      in (thy, result) end;

    val add_recdef = gen_add_recdef Tfl.define Attrib.global_attribute prepare_hints;
    fun add_recdef_i x y z w = gen_add_recdef Tfl.define_i (K I) prepare_hints_i x y z w ();

    (* add_recdef_old -- legacy interface *)

    fun prepare_hints_old thy (ss, thms) =
      let val {simps, congs, wfs} = get_global_hints thy
      in (Classical.claset_of thy, ss addsimps simps, map #2 (add_congs congs thms), wfs) end;

    val add_recdef_old = gen_add_recdef Tfl.define Attrib.global_attribute prepare_hints_old false;

    (** defer_recdef(_i) **)

    fun gen_defer_recdef tfl_fn app_thms raw_name eqs raw_congs thy =
      let
        val name = Sign.intern_const thy raw_name;
        val bname = Sign.base_name name;

        val _ = requires_recdef thy;
        val _ = message ("Deferred recursive function " ^ quote name ^ " ...");

        val (thy1, congs) = thy |> app_thms raw_congs;
        val (thy2, induct_rules) = tfl_fn thy1 congs name eqs;
        val (thy3, [induct_rules']) =
          thy2
          |> Theory.add_path bname
          |> PureThy.add_thms [(("induct_rules", induct_rules), [])]
          |>> Theory.parent_path;
      in (thy3, {induct_rules = induct_rules'}) end;

    val defer_recdef = gen_defer_recdef Tfl.defer IsarThy.apply_theorems;
    val defer_recdef_i = gen_defer_recdef Tfl.defer_i IsarThy.apply_theorems_i;

    (** recdef_tc(_i) **)

    fun gen_recdef_tc prep_att prep_name (bname, raw_atts) raw_name opt_i thy =
      let
        val name = prep_name thy raw_name;
        val atts = map (prep_att thy) raw_atts;
        val tcs =
          (case get_recdef thy name of
            NONE => error ("No recdef definition of constant: " ^ quote name)
          | SOME {tcs, ...} => tcs);
        val i = getOpt (opt_i, 1);
        val tc = List.nth (tcs, i - 1) handle Subscript =>
          error ("No termination condition #" ^ string_of_int i ^
            " in recdef definition of " ^ quote name);
      in IsarThy.theorem_i Drule.internalK (bname, atts) (HOLogic.mk_Trueprop tc, ([], [])) thy end;

    val recdef_tc = gen_recdef_tc Attrib.global_attribute Sign.intern_const;
    val recdef_tc_i = gen_recdef_tc (K I) (K I);

    (** package setup **)

    (* setup theory *)

    val setup =
     [GlobalRecdefData.init, LocalRecdefData.init,
      Attrib.add_attributes
       [(recdef_simpN, simp_attr, "declaration of recdef simp rule"),
        (recdef_congN, cong_attr, "declaration of recdef cong rule"),
        (recdef_wfN, wf_attr, "declaration of recdef wf rule")]];

    (* outer syntax *)

    local structure P = OuterParse and K = OuterKeyword in

    val hints =
      P.$$$ "(" |-- P.!!! (P.position (P.$$$ "hints" -- P.arguments) --| P.$$$ ")") >> Args.src;

    val recdef_decl =
      Scan.optional (P.$$$ "(" -- P.!!! (P.$$$ "permissive" -- P.$$$ ")") >> K false) true --
      P.name -- P.term -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop) -- Scan.option hints
      >> (fn ((((p, f), R), eqs), src) => #1 o add_recdef p f R (map P.triple_swap eqs) src);

    val recdefP =
      OuterSyntax.command "recdef" "define general recursive functions (TFL)" K.thy_decl
        (recdef_decl >> Toplevel.theory);

    val defer_recdef_decl =
      P.name -- Scan.repeat1 P.prop --
      Scan.optional (P.$$$ "(" |-- P.$$$ "congs" |-- P.!!! (P.xthms1 --| P.$$$ ")")) []
      >> (fn ((f, eqs), congs) => #1 o defer_recdef f eqs congs);

    val defer_recdefP =
      OuterSyntax.command "defer_recdef" "defer general recursive functions (TFL)" K.thy_decl
        (defer_recdef_decl >> Toplevel.theory);

    val recdef_tcP =
      OuterSyntax.command "recdef_tc" "recommence proof of termination condition (TFL)" K.thy_goal
        (P.opt_thm_name ":" -- P.xname -- Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")")
          >> (fn ((thm_name, name), i) =>
            Toplevel.print o Toplevel.theory_to_proof (recdef_tc thm_name name i)));

    val _ = OuterSyntax.add_keywords ["permissive", "congs", "hints"];
    val _ = OuterSyntax.add_parsers [recdefP, defer_recdefP, recdef_tcP];

    end;

    end;