(*  Title:      HOL/Tools/recdef_package.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

Wrapper module for Konrad Slind's TFL package.

*)

signature RECDEF_PACKAGE =

sig

  val quiet_mode: bool ref

  val get_recdef: theory -> string

    -> {simps: thm list, rules: thm list list, induct: thm, tcs: term list} option

  val get_hints: Proof.context -> {simps: thm list, congs: (string * thm) list, wfs: thm list}

  val simp_add: attribute

  val simp_del: attribute

  val cong_add: attribute

  val cong_del: attribute

  val wf_add: attribute

  val wf_del: 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) * attribute list) 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 * attribute list) list

    -> theory -> theory * {induct_rules: thm}

  val recdef_tc: bstring * Attrib.src list -> xstring -> int option -> bool -> local_theory -> Proof.state

  val recdef_tc_i: bstring * Attrib.src list -> string -> int option -> bool -> local_theory -> Proof.state

  val setup: theory -> theory

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 snd 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;

    val _ = if AList.defined (op =) congs c

      then warning ("Overwriting recdef congruence rule for " ^ quote c)

      else ();

  in AList.update (op =) (c, thm) congs end;

fun del_cong raw_thm congs =

  let

    val (c, thm) = prep_cong raw_thm;

    val _ = if AList.defined (op =) congs c

      then ()

      else warning ("No recdef congruence rule for " ^ quote c);

  in AList.delete (op =) c congs end;

end;

(** global and local recdef data **)

(* theory data *)

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

structure GlobalRecdefData = TheoryDataFun

(

  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 (Thm.merge_thms (simps1, simps2),

          AList.merge (op =) Thm.eq_thm (congs1, congs2),

          Thm.merge_thms (wfs1, wfs2)));

);

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;

(* proof data *)

structure LocalRecdefData = ProofDataFun

(

  type T = hints;

  val init = get_global_hints;

);

val get_hints = LocalRecdefData.get;

fun map_hints f = Context.mapping (GlobalRecdefData.map (apsnd f)) (LocalRecdefData.map f);

(* attributes *)

fun attrib f = Thm.declaration_attribute (map_hints o f);

val simp_add = attrib (map_simps o Thm.add_thm);

val simp_del = attrib (map_simps o Thm.del_thm);

val cong_add = attrib (map_congs o add_cong);

val cong_del = attrib (map_congs o del_cong);

val wf_add = attrib (map_wfs o Thm.add_thm);

val wf_del = attrib (map_wfs o Thm.del_thm);

(* 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): Method.modifier),

  Args.$$$ recdef_simpN -- Args.add -- Args.colon >> K (I, simp_add),

  Args.$$$ recdef_simpN -- Args.del -- Args.colon >> K (I, simp_del),

  Args.$$$ recdef_congN -- Args.colon >> K (I, cong_add),

  Args.$$$ recdef_congN -- Args.add -- Args.colon >> K (I, cong_add),

  Args.$$$ recdef_congN -- Args.del -- Args.colon >> K (I, cong_del),

  Args.$$$ recdef_wfN -- Args.colon >> K (I, wf_add),

  Args.$$$ recdef_wfN -- Args.add -- Args.colon >> K (I, wf_add),

  Args.$$$ recdef_wfN -- Args.del -- Args.colon >> K (I, wf_del)] @

  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_hints ctxt;

    val cs = local_claset_of ctxt;

    val ss = local_simpset_of ctxt addsimps simps;

  in (cs, ss, rev (map snd 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, rev (map snd congs), wfs) end;

(** add_recdef(_i) **)

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

fun gen_add_recdef tfl_fn prep_att prep_hints not_permissive 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 not_permissive thy cs (ss delcongs [imp_cong])

               congs wfs name R eqs;

    val rules = (map o map) fst (partition_eq (eq_snd (op = : int * int -> bool)) rules_idx);

    val simp_att = if null tcs then [Simplifier.simp_add, RecfunCodegen.add_default] else [];

    val ((simps' :: rules', [induct']), thy) =

      thy

      |> Sign.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

      |> Sign.parent_path;

  in (thy, result) end;

val add_recdef = gen_add_recdef Tfl.define Attrib.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 ();

(** 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 (congs, thy1) = thy |> app_thms raw_congs;

    val (thy2, induct_rules) = tfl_fn thy1 congs name eqs;

    val ([induct_rules'], thy3) =

      thy2

      |> Sign.add_path bname

      |> PureThy.add_thms [(("induct_rules", induct_rules), [])]

      ||> Sign.parent_path;

  in (thy3, {induct_rules = induct_rules'}) end;

val defer_recdef = gen_defer_recdef Tfl.defer IsarCmd.apply_theorems;

val defer_recdef_i = gen_defer_recdef Tfl.defer_i IsarCmd.apply_theorems_i;

(** recdef_tc(_i) **)

fun gen_recdef_tc prep_att prep_name (bname, raw_atts) raw_name opt_i int lthy =

  let

    val thy = ProofContext.theory_of lthy;

    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 = the_default 1 opt_i;

    val tc = nth tcs (i - 1) handle Subscript =>

      error ("No termination condition #" ^ string_of_int i ^

        " in recdef definition of " ^ quote name);

  in

    Specification.theorem_i Thm.internalK NONE (K I) (bname, atts)

      [] (Element.Shows [(("", []), [(HOLogic.mk_Trueprop tc, [])])]) int lthy

  end;

val recdef_tc = gen_recdef_tc Attrib.intern_src Sign.intern_const;

val recdef_tc_i = gen_recdef_tc (K I) (K I);

(** package setup **)

(* setup theory *)

val setup =

  Attrib.add_attributes

   [(recdef_simpN, Attrib.add_del_args simp_add simp_del, "declaration of recdef simp rule"),

    (recdef_congN, Attrib.add_del_args cong_add cong_del, "declaration of recdef cong rule"),

    (recdef_wfN, Attrib.add_del_args wf_add wf_del, "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 (SpecParse.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.!!! (SpecParse.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_target --

      SpecParse.opt_thm_name ":" -- P.xname -- Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")")

      >> (fn (((loc, thm_name), name), i) =>

        Toplevel.print o Toplevel.local_theory_to_proof' loc (recdef_tc thm_name name i)));

val _ = OuterSyntax.add_keywords ["permissive", "congs", "hints"];

val _ = OuterSyntax.add_parsers [recdefP, defer_recdefP, recdef_tcP];

end;

end;