(*  Title:      HOL/Tools/recdef.ML

     Author:     Markus Wenzel, TU Muenchen

 Wrapper module for Konrad Slind's TFL package.

 *)

 signature RECDEF =

 sig

   val get_recdef: theory -> string

     -> {lhs: term, 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 -> ((binding * string) * Attrib.src list) list ->

     Attrib.src option -> theory -> theory

       * {lhs: term, simps: thm list, rules: thm list list, induct: thm, tcs: term list}

   val add_recdef_i: bool -> xstring -> term -> ((binding * term) * attribute list) list ->

     theory -> theory * {lhs: term, simps: thm list, rules: thm list list, induct: thm, tcs: term list}

   val defer_recdef: xstring -> string list -> (Facts.ref * Attrib.src list) list

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

   val defer_recdef_i: xstring -> term list -> thm 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 Recdef: RECDEF =

 struct

 (** 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));

 (* 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 = {lhs: term, simps: thm list, rules: thm list list, induct: thm, tcs: term list};

 structure GlobalRecdefData = Theory_Data

 (

   type T = recdef_info Symtab.table * hints;

   val empty = (Symtab.empty, mk_hints ([], [], [])): T;

   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 =) (K true) (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 = Proof_Data

 (

   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 = Proof_Context.init_global thy;

     val ctxt =

       (case opt_src of

         NONE => ctxt0

       | SOME src => #2 (Method.syntax (Method.sections recdef_modifiers) src ctxt0));

     val {simps, congs, wfs} = get_hints ctxt;

     val ctxt' = ctxt

       |> Simplifier.map_simpset (fn ss => ss addsimps simps |> Simplifier.del_cong @{thm imp_cong});

   in (ctxt', rev (map snd congs), wfs) end;

 fun prepare_hints_i thy () =

   let

     val ctxt = Proof_Context.init_global thy;

     val {simps, congs, wfs} = get_global_hints thy;

     val ctxt' = ctxt

       |> Simplifier.map_simpset (fn ss => ss addsimps simps |> Simplifier.del_cong @{thm imp_cong});

   in (ctxt', rev (map snd congs), wfs) end;

 (** add_recdef(_i) **)

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

 fun gen_add_recdef tfl_fn prep_att prep_hints not_permissive raw_name R eq_srcs hints thy =

   let

     val _ = legacy_feature "Old 'recdef' command -- use 'fun' or 'function' instead";

     val _ = requires_recdef thy;

     val name = Sign.intern_const thy raw_name;

     val bname = Long_Name.base_name name;

     val _ = writeln ("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 (ctxt, 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 ({lhs, rules = rules_idx, induct, tcs}, thy) =

       tfl_fn not_permissive ctxt congs wfs name R eqs thy;

     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, Nitpick_Simps.add, Code.add_default_eqn_attribute]

       else [];

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

       thy

       |> Sign.add_path bname

       |> Global_Theory.add_thmss

         (((Binding.name "simps", flat rules), simp_att) :: ((eq_names ~~ rules) ~~ eq_atts))

       ||>> Global_Theory.add_thms [((Binding.name "induct", induct), [])]

       ||> Spec_Rules.add_global Spec_Rules.Equational ([lhs], flat rules);

     val result = {lhs = lhs, 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 eval_thms raw_name eqs raw_congs thy =

   let

     val name = Sign.intern_const thy raw_name;

     val bname = Long_Name.base_name name;

     val _ = requires_recdef thy;

     val _ = writeln ("Deferred recursive function " ^ quote name ^ " ...");

     val congs = eval_thms (Proof_Context.init_global thy) raw_congs;

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

     val ([induct_rules'], thy3) =

       thy2

       |> Sign.add_path bname

       |> Global_Theory.add_thms [((Binding.name "induct_rules", induct_rules), [])]

       ||> Sign.parent_path;

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

 val defer_recdef = gen_defer_recdef Tfl.defer Attrib.eval_thms;

 val defer_recdef_i = gen_defer_recdef Tfl.defer_i (K I);

 (** recdef_tc(_i) **)

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

   let

     val thy = Proof_Context.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 General.Subscript =>

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

         " in recdef definition of " ^ quote name);

   in

     Specification.theorem "" NONE (K I)

       (Binding.conceal (Binding.name bname), atts) []

       (Element.Shows [(Attrib.empty_binding, [(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.setup @{binding recdef_simp} (Attrib.add_del simp_add simp_del)

     "declaration of recdef simp rule" #>

   Attrib.setup @{binding recdef_cong} (Attrib.add_del cong_add cong_del)

     "declaration of recdef cong rule" #>

   Attrib.setup @{binding recdef_wf} (Attrib.add_del wf_add wf_del)

     "declaration of recdef wf rule";

 (* outer syntax *)

 val hints =

   @{keyword "("} |--

     Parse.!!! (Parse.position (@{keyword "hints"} -- Args.parse) --| @{keyword ")"}) >> Args.src;

 val recdef_decl =

   Scan.optional

     (@{keyword "("} -- Parse.!!! (@{keyword "permissive"} -- @{keyword ")"}) >> K false) true --

   Parse.name -- Parse.term -- Scan.repeat1 (Parse_Spec.opt_thm_name ":" -- Parse.prop)

     -- Scan.option hints

   >> (fn ((((p, f), R), eqs), src) => #1 o add_recdef p f R (map Parse.triple_swap eqs) src);

 val _ =

   Outer_Syntax.command "recdef" "define general recursive functions (TFL)" Keyword.thy_decl

     (recdef_decl >> Toplevel.theory);

 val defer_recdef_decl =

   Parse.name -- Scan.repeat1 Parse.prop --

   Scan.optional

     (@{keyword "("} |-- @{keyword "congs"} |-- Parse.!!! (Parse_Spec.xthms1 --| @{keyword ")"})) []

   >> (fn ((f, eqs), congs) => #1 o defer_recdef f eqs congs);

 val _ =

   Outer_Syntax.command "defer_recdef" "defer general recursive functions (TFL)" Keyword.thy_decl

     (defer_recdef_decl >> Toplevel.theory);

 val _ =

   Outer_Syntax.local_theory_to_proof' "recdef_tc" "recommence proof of termination condition (TFL)"

     Keyword.thy_goal

     ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.xname --

         Scan.option (@{keyword "("} |-- Parse.nat --| @{keyword ")"})

       >> (fn ((thm_name, name), i) => recdef_tc thm_name name i));

 end;