path: root/tactics/auto.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open Util
open Names
open Nameops
open Namegen
open Term
open Termops
open Inductiveops
open Sign
open Environ
open Inductive
open Evd
open Reduction
open Typing
open Pattern
open Matching
open Tacmach
open Proof_type
open Pfedit
open Glob_term
open Evar_refiner
open Tacred
open Tactics
open Tacticals
open Clenv
open Hiddentac
open Libnames
open Nametab
open Smartlocate
open Libobject
open Library
open Printer
open Declarations
open Tacexpr
open Mod_subst

(****************************************************************************)
(*            The Type of Constructions Autotactic Hints                    *)
(****************************************************************************)

type 'a auto_tactic =
  | Res_pf     of constr * 'a (* Hint Apply *)
  | ERes_pf    of constr * 'a (* Hint EApply *)
  | Give_exact of constr
  | Res_pf_THEN_trivial_fail of constr * 'a (* Hint Immediate *)
  | Unfold_nth of evaluable_global_reference       (* Hint Unfold *)
  | Extern     of glob_tactic_expr       (* Hint Extern *)

type hints_path_atom = 
  | PathHints of global_reference list
  | PathAny

type hints_path =
  | PathAtom of hints_path_atom
  | PathStar of hints_path
  | PathSeq of hints_path * hints_path
  | PathOr of hints_path * hints_path
  | PathEmpty
  | PathEpsilon

type 'a gen_auto_tactic = {
  pri  : int;            (* A number lower is higher priority *)
  pat  : constr_pattern option; (* A pattern for the concl of the Goal *)
  name  : hints_path_atom; (* A potential name to refer to the hint *) 
  code : 'a auto_tactic     (* the tactic to apply when the concl matches pat *)
}

type pri_auto_tactic = clausenv gen_auto_tactic

type hint_entry = global_reference option * types gen_auto_tactic

let pri_order_int (id1, {pri=pri1}) (id2, {pri=pri2}) =
  let d = pri1 - pri2 in
    if d == 0 then id2 - id1
    else d

let pri_order t1 t2 = pri_order_int t1 t2 <= 0

let insert v l =
  let rec insrec = function
    | [] -> [v]
    | h::tl -> if pri_order v h then v::h::tl else h::(insrec tl)
  in
  insrec l

(* Nov 98 -- Papageno *)
(* Les Hints sont ré-organisés en plusieurs databases.

  La table impérative "searchtable", de type "hint_db_table",
   associe une database (hint_db) à chaque nom.

  Une hint_db est une table d'association fonctionelle constr -> search_entry
  Le constr correspond à la constante de tête de la conclusion.

  Une search_entry est un triplet comprenant :
     - la liste des tactiques qui n'ont pas de pattern associé
     - la liste des tactiques qui ont un pattern
     - un discrimination net borné (Btermdn.t) constitué de tous les
       patterns de la seconde liste de tactiques *)

type stored_data = int * pri_auto_tactic
    (* First component is the index of insertion in the table, to keep most recent first semantics. *)

let auto_tactic_ord code1 code2 =
  match code1, code2 with
  | Res_pf (c1, _), Res_pf (c2, _)
  | ERes_pf (c1, _), ERes_pf (c2, _)
  | Give_exact c1, Give_exact c2
  | Res_pf_THEN_trivial_fail (c1, _), Res_pf_THEN_trivial_fail (c2, _) -> constr_ord c1 c2
  | Unfold_nth (EvalVarRef i1), Unfold_nth (EvalVarRef i2) -> Pervasives.compare i1 i2
  | Unfold_nth (EvalConstRef c1), Unfold_nth (EvalConstRef c2) ->
      kn_ord (canonical_con c1) (canonical_con c2)
  | Extern t1, Extern t2 -> Pervasives.compare t1 t2
  | _ -> Pervasives.compare code1 code2

module Bounded_net = Btermdn.Make(struct
				    type t = stored_data
				    let compare = pri_order_int
				  end)

type search_entry = stored_data list * stored_data list * Bounded_net.t

let empty_se = ([],[],Bounded_net.create ())

let eq_pri_auto_tactic (_, x) (_, y) =
  if x.pri = y.pri && x.pat = y.pat then
    match x.code,y.code with
      | Res_pf(cstr,_),Res_pf(cstr1,_) -> 
	   eq_constr cstr cstr1
      | ERes_pf(cstr,_),ERes_pf(cstr1,_) -> 
	  eq_constr cstr cstr1
      | Give_exact cstr,Give_exact cstr1  -> 
	  eq_constr cstr cstr1
      | Res_pf_THEN_trivial_fail(cstr,_)
	  ,Res_pf_THEN_trivial_fail(cstr1,_) -> 
	  eq_constr cstr cstr1
      | _,_ -> false
  else
    false

let add_tac pat t st (l,l',dn) =
  match pat with
  | None -> if not (List.exists (eq_pri_auto_tactic t) l) then (insert t l, l', dn) else (l, l', dn)
  | Some pat -> 
    if not (List.exists (eq_pri_auto_tactic t) l') 
    then (l, insert t l', Bounded_net.add st dn (pat,t)) else (l, l', dn)

let rebuild_dn st ((l,l',dn) : search_entry) =
  (l, l', List.fold_left (fun dn (id, t) -> Bounded_net.add (Some st) dn (Option.get t.pat, (id, t)))
    (Bounded_net.create ()) l')


let lookup_tacs (hdc,c) st (l,l',dn) =
  let l'  = List.map snd (Bounded_net.lookup st dn c) in
  let sl' = List.stable_sort pri_order_int l' in
    Sort.merge pri_order l sl'

module Constr_map = Map.Make(RefOrdered)

let is_transparent_gr (ids, csts) = function
  | VarRef id -> Idpred.mem id ids
  | ConstRef cst -> Cpred.mem cst csts
  | IndRef _ | ConstructRef _ -> false

let dummy_goal = Goal.V82.dummy_goal

let translate_hint (go,p) =
  let mk_clenv (c,t) =
    let cl = mk_clenv_from dummy_goal (c,t) in {cl with env = empty_env }
  in
  let code = match p.code with
    | Res_pf (c,t) -> Res_pf (c, mk_clenv (c,t))
    | ERes_pf (c,t) -> ERes_pf (c, mk_clenv (c,t))
    | Res_pf_THEN_trivial_fail (c,t) ->
      Res_pf_THEN_trivial_fail (c, mk_clenv (c,t))
    | Give_exact c -> Give_exact c
    | Unfold_nth e -> Unfold_nth e
    | Extern t -> Extern t
  in
  (go,{ p with code = code })

let path_matches hp hints =
  let rec aux hp hints k =
    match hp, hints with
    | PathAtom _, [] -> false
    | PathAtom PathAny, (_ :: hints') -> k hints'
    | PathAtom p, (h :: hints') -> 
      if p = h then k hints' else false
    | PathStar hp', hints -> 
      k hints || aux hp' hints (fun hints' -> aux hp hints' k)
    | PathSeq (hp, hp'), hints -> 
      aux hp hints (fun hints' -> aux hp' hints' k)
    | PathOr (hp, hp'), hints ->
      aux hp hints k || aux hp' hints k
    | PathEmpty, _ -> false
    | PathEpsilon, hints -> k hints
  in aux hp hints (fun hints' -> true)

let rec matches_epsilon = function
  | PathAtom _ -> false
  | PathStar _ -> true
  | PathSeq (p, p') -> matches_epsilon p && matches_epsilon p'
  | PathOr (p, p') -> matches_epsilon p || matches_epsilon p'
  | PathEmpty -> false
  | PathEpsilon -> true

let rec is_empty = function
  | PathAtom _ -> false
  | PathStar _ -> false
  | PathSeq (p, p') -> is_empty p || is_empty p'
  | PathOr (p, p') -> matches_epsilon p && matches_epsilon p'
  | PathEmpty -> true
  | PathEpsilon -> false

let rec path_derivate hp hint =
  let rec derivate_atoms hints hints' =
    match hints, hints' with
    | gr :: grs, gr' :: grs' when gr = gr' -> derivate_atoms grs grs'
    | [], [] -> PathEpsilon
    | [], hints -> PathEmpty
    | grs, [] -> PathAtom (PathHints grs)
    | _, _ -> PathEmpty 
  in
    match hp with
    | PathAtom PathAny -> PathEpsilon
    | PathAtom (PathHints grs) -> 
      (match grs, hint with
       | h :: hints, PathAny -> PathEmpty
       | hints, PathHints hints' -> derivate_atoms hints hints'
       | _, _ -> assert false)
    | PathStar p -> if path_matches p [hint] then hp else PathEpsilon
    | PathSeq (hp, hp') ->
      let hpder = path_derivate hp hint in
	if matches_epsilon hp then 
	  PathOr (PathSeq (hpder, hp'), path_derivate hp' hint)
	else if is_empty hpder then PathEmpty 
	else PathSeq (hpder, hp')
    | PathOr (hp, hp') ->
      PathOr (path_derivate hp hint, path_derivate hp' hint)
    | PathEmpty -> PathEmpty
    | PathEpsilon -> PathEmpty

let rec normalize_path h =
  match h with
  | PathStar PathEpsilon -> PathEpsilon
  | PathSeq (PathEmpty, _) | PathSeq (_, PathEmpty) -> PathEmpty
  | PathSeq (PathEpsilon, p) | PathSeq (p, PathEpsilon) -> normalize_path p
  | PathOr (PathEmpty, p) | PathOr (p, PathEmpty) -> normalize_path p
  | PathOr (p, q) -> 
    let p', q' = normalize_path p, normalize_path q in
      if p = p' && q = q' then h
      else normalize_path (PathOr (p', q'))
  | PathSeq (p, q) -> 
    let p', q' = normalize_path p, normalize_path q in
      if p = p' && q = q' then h
      else normalize_path (PathSeq (p', q'))
  | _ -> h

let path_derivate hp hint = normalize_path (path_derivate hp hint)

let rec pp_hints_path = function
  | PathAtom (PathAny) -> str"."
  | PathAtom (PathHints grs) -> prlist_with_sep pr_spc pr_global grs
  | PathStar p -> str "(" ++ pp_hints_path p ++ str")*"
  | PathSeq (p, p') -> pp_hints_path p ++ str" ; " ++ pp_hints_path p'
  | PathOr (p, p') -> 
    str "(" ++ pp_hints_path p ++ spc () ++ str"|" ++ spc () ++ pp_hints_path p' ++ str ")"
  | PathEmpty -> str"Ø"
  | PathEpsilon -> str"ε"

let rec subst_hints_path subst hp =
  match hp with
  | PathAtom PathAny -> hp
  | PathAtom (PathHints grs) -> 
    let gr' gr = fst (subst_global subst gr) in
    let grs' = list_smartmap gr' grs in
      if grs' == grs then hp else PathAtom (PathHints grs')
  | PathStar p -> let p' = subst_hints_path subst p in
      if p' == p then hp else PathStar p'
  | PathSeq (p, q) ->
    let p' = subst_hints_path subst p in
    let q' = subst_hints_path subst q in
      if p' == p && q' == q then hp else PathSeq (p', q')
  | PathOr (p, q) ->
    let p' = subst_hints_path subst p in
    let q' = subst_hints_path subst q in
      if p' == p && q' == q then hp else PathOr (p', q')
  | _ -> hp

module Hint_db = struct

  type t = {
    hintdb_state : Names.transparent_state;
    hintdb_cut : hints_path;
    hintdb_unfolds : Idset.t * Cset.t;
    mutable hintdb_max_id : int;
    use_dn : bool;
    hintdb_map : search_entry Constr_map.t;
    (* A list of unindexed entries starting with an unfoldable constant
       or with no associated pattern. *)
    hintdb_nopat : (global_reference option * stored_data) list
  }

  let next_hint_id t = 
    let h = t.hintdb_max_id in t.hintdb_max_id <- succ t.hintdb_max_id; h

  let empty st use_dn = { hintdb_state = st;
			  hintdb_cut = PathEmpty;
			  hintdb_unfolds = (Idset.empty, Cset.empty);
			  hintdb_max_id = 0;
			  use_dn = use_dn;
			  hintdb_map = Constr_map.empty;
			  hintdb_nopat = [] }

  let find key db =
    try Constr_map.find key db.hintdb_map
    with Not_found -> empty_se
 
  let map_none db =
    List.map snd (Sort.merge pri_order (List.map snd db.hintdb_nopat) [])
    
  let map_all k db =
    let (l,l',_) = find k db in
      List.map snd (Sort.merge pri_order (List.map snd db.hintdb_nopat @ l) l')

  let map_auto (k,c) db =
    let st = if db.use_dn then Some db.hintdb_state else None in
    let l' = lookup_tacs (k,c) st (find k db) in
      List.map snd (Sort.merge pri_order (List.map snd db.hintdb_nopat) l')

  let is_exact = function
    | Give_exact _ -> true
    | _ -> false

  let is_unfold = function
    | Unfold_nth _ -> true
    | _ -> false

  let addkv gr id v db =
    let idv = id, v in
    let k = match gr with
      | Some gr -> if db.use_dn && is_transparent_gr db.hintdb_state gr &&
	  is_unfold v.code then None else Some gr
      | None -> None
    in
    let dnst = if db.use_dn then Some db.hintdb_state else None in
    let pat = if not db.use_dn && is_exact v.code then None else v.pat in
      match k with
      | None ->
	  if not (List.exists (fun (_, (_, v')) -> v = v') db.hintdb_nopat) then
	    { db with hintdb_nopat = (gr,idv) :: db.hintdb_nopat }
	  else db
      | Some gr ->
	  let oval = find gr db in
	    { db with hintdb_map = Constr_map.add gr (add_tac pat idv dnst oval) db.hintdb_map }

  let rebuild_db st' db =
    let db' =
      { db with hintdb_map = Constr_map.map (rebuild_dn st') db.hintdb_map;
	hintdb_state = st'; hintdb_nopat = [] }
    in
      List.fold_left (fun db (gr,(id,v)) -> addkv gr id v db) db' db.hintdb_nopat

  let add_one kv db =
    let (k,v) = translate_hint kv in
    let st',db,rebuild =
      match v.code with
      | Unfold_nth egr ->
	  let addunf (ids,csts) (ids',csts') =
	    match egr with
	    | EvalVarRef id -> (Idpred.add id ids, csts), (Idset.add id ids', csts')
	    | EvalConstRef cst -> (ids, Cpred.add cst csts), (ids', Cset.add cst csts')
	  in 
	  let state, unfs = addunf db.hintdb_state db.hintdb_unfolds in
	    state, { db with hintdb_unfolds = unfs }, true
      | _ -> db.hintdb_state, db, false
    in
    let db = if db.use_dn && rebuild then rebuild_db st' db else db
    in addkv k (next_hint_id db) v db

  let add_list l db = List.fold_right add_one l db

  let remove_sdl p sdl = list_smartfilter p sdl 
  let remove_he st p (sl1, sl2, dn as he) =
    let sl1' = remove_sdl p sl1 and sl2' = remove_sdl p sl2 in
      if sl1' == sl1 && sl2' == sl2 then he
      else rebuild_dn st (sl1', sl2', dn)

  let remove_list grs db =
    let filter (_, h) = match h.name with PathHints [gr] -> not (List.mem gr grs) | _ -> true in
    let hintmap = Constr_map.map (remove_he db.hintdb_state filter) db.hintdb_map in
    let hintnopat = list_smartfilter (fun (ge, sd) -> filter sd) db.hintdb_nopat in
      { db with hintdb_map = hintmap; hintdb_nopat = hintnopat }

  let remove_one gr db = remove_list [gr] db

  let iter f db =
    f None (List.map (fun x -> snd (snd x)) db.hintdb_nopat);
    Constr_map.iter (fun k (l,l',_) -> f (Some k) (List.map snd (l@l'))) db.hintdb_map

  let transparent_state db = db.hintdb_state

  let set_transparent_state db st =
    if db.use_dn then rebuild_db st db
    else { db with hintdb_state = st }

  let add_cut path db =
    { db with hintdb_cut = normalize_path (PathOr (db.hintdb_cut, path)) }

  let cut db = db.hintdb_cut

  let unfolds db = db.hintdb_unfolds

  let use_dn db = db.use_dn

end

module Hintdbmap = Gmap

type hint_db = Hint_db.t

type frozen_hint_db_table = (string,hint_db) Hintdbmap.t

type hint_db_table = (string,hint_db) Hintdbmap.t ref

type hint_db_name = string

let searchtable = (ref Hintdbmap.empty : hint_db_table)

let searchtable_map name =
  Hintdbmap.find name !searchtable
let searchtable_add (name,db) =
  searchtable := Hintdbmap.add name db !searchtable
let current_db_names () =
  Hintdbmap.dom !searchtable

(**************************************************************************)
(*                       Definition of the summary                        *)
(**************************************************************************)

let auto_init : (unit -> unit) ref = ref (fun () -> ())
let add_auto_init f = 
  let init = !auto_init in
    auto_init := (fun () -> init (); f ())

let init     () = searchtable := Hintdbmap.empty; !auto_init ()
let freeze   () = !searchtable
let unfreeze fs = searchtable := fs

let _ = Summary.declare_summary "search"
	  { Summary.freeze_function   = freeze;
	    Summary.unfreeze_function = unfreeze;
	    Summary.init_function     = init }


(**************************************************************************)
(*             Auxiliary functions to prepare AUTOHINT objects            *)
(**************************************************************************)

let rec nb_hyp c = match kind_of_term c with
  | Prod(_,_,c2) -> if noccurn 1 c2 then 1+(nb_hyp c2) else nb_hyp c2
  | _ -> 0

(* adding and removing tactics in the search table *)

let try_head_pattern c =
  try head_pattern_bound c
  with BoundPattern -> error "Bound head variable."

let name_of_constr c = try Some (global_of_constr c) with Not_found -> None

let make_exact_entry sigma pri ?(name=PathAny) (c,cty) =
  let cty = strip_outer_cast cty in
    match kind_of_term cty with
    | Prod _ -> failwith "make_exact_entry"
    | _ ->
	let pat = snd (Pattern.pattern_of_constr sigma cty) in
	let hd =
	  try head_pattern_bound pat
	  with BoundPattern -> failwith "make_exact_entry"
	in
          (Some hd,
	  { pri = (match pri with None -> 0 | Some p -> p);
	    pat = Some pat;
	    name = name;
	    code = Give_exact c })

let make_apply_entry env sigma (eapply,hnf,verbose) pri ?(name=PathAny) (c,cty) =
  let cty = if hnf then hnf_constr env sigma cty else cty in
    match kind_of_term cty with
    | Prod _ ->
        let ce = mk_clenv_from dummy_goal (c,cty) in
	let c' = clenv_type (* ~reduce:false *) ce in
	let pat = snd (Pattern.pattern_of_constr sigma c') in
        let hd =
	  try head_pattern_bound pat
          with BoundPattern -> failwith "make_apply_entry" in
        let nmiss = List.length (clenv_missing ce) in
	if nmiss = 0 then
	  (Some hd,
          { pri = (match pri with None -> nb_hyp cty | Some p -> p);
            pat = Some pat;
	    name = name;
            code = Res_pf(c,cty) })
	else begin
	  if not eapply then failwith "make_apply_entry";
          if verbose then
	    warn (str "the hint: eapply " ++ pr_lconstr c ++
	    str " will only be used by eauto");
          (Some hd,
           { pri = (match pri with None -> nb_hyp cty + nmiss | Some p -> p);
             pat = Some pat;
	     name = name;
             code = ERes_pf(c,cty) })
        end
    | _ -> failwith "make_apply_entry"

(* flags is (e,h,v) with e=true if eapply and h=true if hnf and v=true if verbose
   c is a constr
   cty is the type of constr *)

let make_resolves env sigma flags pri ?name c =
  let cty = Retyping.get_type_of env sigma c in
  let ents =
    map_succeed
      (fun f -> f (c,cty))
      [make_exact_entry sigma pri ?name; make_apply_entry env sigma flags pri ?name]
  in
  if ents = [] then
    errorlabstrm "Hint"
      (pr_lconstr c ++ spc() ++
        (if pi1 flags then str"cannot be used as a hint."
	else str "can be used as a hint only for eauto."));
  ents

(* used to add an hypothesis to the local hint database *)
let make_resolve_hyp env sigma (hname,_,htyp) =
  try
    [make_apply_entry env sigma (true, true, false) None 
       ~name:(PathHints [VarRef hname])
       (mkVar hname, htyp)]
  with
    | Failure _ -> []
    | e when Logic.catchable_exception e -> anomaly "make_resolve_hyp"

(* REM : in most cases hintname = id *)
let make_unfold eref =
  let g = global_of_evaluable_reference eref in
  (Some g,
   { pri = 4;
     pat = None;
     name = PathHints [g];
     code = Unfold_nth eref })

let make_extern pri pat tacast =
  let hdconstr = Option.map try_head_pattern pat in
  (hdconstr,
   { pri = pri;
     pat = pat;
     name = PathAny;
     code = Extern tacast })

let make_trivial env sigma ?(name=PathAny) c =
  let t = hnf_constr env sigma (type_of env sigma c) in
  let hd = head_of_constr_reference (fst (head_constr t)) in
  let ce = mk_clenv_from dummy_goal (c,t) in
  (Some hd, { pri=1;
              pat = Some (snd (Pattern.pattern_of_constr sigma (clenv_type ce)));
	      name = name;
              code=Res_pf_THEN_trivial_fail(c,t) })
  
open Vernacexpr

(**************************************************************************)
(*               declaration of the AUTOHINT library object               *)
(**************************************************************************)

(* If the database does not exist, it is created *)
(* TODO: should a warning be printed in this case ?? *)

let get_db dbname =
  try searchtable_map dbname
  with Not_found -> Hint_db.empty empty_transparent_state false

let add_hint dbname hintlist = 
  let db = get_db dbname in
  let db' = Hint_db.add_list hintlist db in
    searchtable_add (dbname,db')

let add_transparency dbname grs b =
  let db = get_db dbname in
  let st = Hint_db.transparent_state db in
  let st' =
    List.fold_left (fun (ids, csts) gr ->
      match gr with
      | EvalConstRef c -> (ids, (if b then Cpred.add else Cpred.remove) c csts)
      | EvalVarRef v -> (if b then Idpred.add else Idpred.remove) v ids, csts)
      st grs
  in searchtable_add (dbname, Hint_db.set_transparent_state db st')

let remove_hint dbname grs =
  let db = get_db dbname in
  let db' = Hint_db.remove_list grs db in
    searchtable_add (dbname, db')

type hint_action =
  | CreateDB of bool * transparent_state
  | AddTransparency of evaluable_global_reference list * bool
  | AddHints of hint_entry list
  | RemoveHints of global_reference list
  | AddCut of hints_path

let add_cut dbname path =
  let db = get_db dbname in
  let db' = Hint_db.add_cut path db in
    searchtable_add (dbname, db')

type hint_obj = bool * string * hint_action  (* locality, name, action *)

let cache_autohint (_,(local,name,hints)) =
  match hints with
  | CreateDB (b, st) -> searchtable_add (name, Hint_db.empty st b)
  | AddTransparency (grs, b) -> add_transparency name grs b
  | AddHints hints -> add_hint name hints
  | RemoveHints grs -> remove_hint name grs
  | AddCut path -> add_cut name path

let forward_subst_tactic =
  ref (fun _ -> failwith "subst_tactic is not installed for auto")

let set_extern_subst_tactic f = forward_subst_tactic := f

let subst_autohint (subst,(local,name,hintlist as obj)) =
  let subst_key gr =
    let (lab'', elab') = subst_global subst gr in
    let gr' =
      (try head_of_constr_reference (fst (head_constr_bound elab'))
       with Tactics.Bound -> lab'')
    in if gr' == gr then gr else gr'
  in
  let subst_hint (k,data as hint) =
    let k' = Option.smartmap subst_key k in
    let pat' = Option.smartmap (subst_pattern subst) data.pat in
    let code' = match data.code with
      | Res_pf (c,t) ->
          let c' = subst_mps subst c in
          let t' = subst_mps subst t in
          if c==c' && t'==t then data.code else Res_pf (c', t')
      | ERes_pf (c,t) ->
          let c' = subst_mps subst c in
          let t' = subst_mps subst t in
          if c==c' && t'==t then data.code else ERes_pf (c',t')
      | Give_exact c ->
          let c' = subst_mps subst c in
          if c==c' then data.code else Give_exact c'
      | Res_pf_THEN_trivial_fail (c,t) ->
          let c' = subst_mps subst c in
          let t' = subst_mps subst t in
          if c==c' && t==t' then data.code else Res_pf_THEN_trivial_fail (c',t')
      | Unfold_nth ref ->
          let ref' = subst_evaluable_reference subst ref in
          if ref==ref' then data.code else Unfold_nth ref'
      | Extern tac ->
	  let tac' = !forward_subst_tactic subst tac in
	  if tac==tac' then data.code else Extern tac'
    in
    let data' =
      if data.pat==pat' && data.code==code' then data
      else { data with pat = pat'; code = code' }
    in
    if k' == k && data' == data then hint else (k',data')
  in
    match hintlist with
    | CreateDB _ -> obj
    | AddTransparency (grs, b) ->
	let grs' = list_smartmap (subst_evaluable_reference subst) grs in
	  if grs==grs' then obj else (local, name, AddTransparency (grs', b))
    | AddHints hintlist ->
	let hintlist' = list_smartmap subst_hint hintlist in
	  if hintlist' == hintlist then obj else
	    (local,name,AddHints hintlist')
    | RemoveHints grs ->
	let grs' = list_smartmap (fun x -> fst (subst_global subst x)) grs in
	  if grs==grs' then obj else (local, name, RemoveHints grs')
    | AddCut path ->
      let path' = subst_hints_path subst path in
	if path' == path then obj else (local, name, AddCut path')

let classify_autohint ((local,name,hintlist) as obj) =
  if local or hintlist = (AddHints []) then Dispose else Substitute obj

let inAutoHint : hint_obj -> obj =
  declare_object {(default_object "AUTOHINT") with
                    cache_function = cache_autohint;
		    load_function = (fun _ -> cache_autohint);
		    subst_function = subst_autohint;
		    classify_function = classify_autohint; }

let create_hint_db l n st b =
  Lib.add_anonymous_leaf (inAutoHint (l,n,CreateDB (b, st)))

let remove_hints local dbnames grs =
  let dbnames = if dbnames = [] then ["core"] else dbnames in
    List.iter
      (fun dbname ->
	 Lib.add_anonymous_leaf (inAutoHint(local, dbname, RemoveHints grs)))
      dbnames

(**************************************************************************)
(*                     The "Hint" vernacular command                      *)
(**************************************************************************)
let add_resolves env sigma clist local dbnames =
  List.iter
    (fun dbname ->
       Lib.add_anonymous_leaf
	 (inAutoHint
	    (local,dbname, AddHints
     	      (List.flatten (List.map (fun (x, hnf, path, y) ->
		make_resolves env sigma (true,hnf,Flags.is_verbose()) x ~name:path y) clist)))))
    dbnames

let add_unfolds l local dbnames =
  List.iter
    (fun dbname -> Lib.add_anonymous_leaf
       (inAutoHint (local,dbname, AddHints (List.map make_unfold l))))
    dbnames

let add_cuts l local dbnames =
  List.iter
    (fun dbname -> Lib.add_anonymous_leaf
       (inAutoHint (local,dbname, AddCut l)))
    dbnames

let add_transparency l b local dbnames =
  List.iter
    (fun dbname -> Lib.add_anonymous_leaf
       (inAutoHint (local,dbname, AddTransparency (l, b))))
    dbnames

let add_extern pri pat tacast local dbname =
  (* We check that all metas that appear in tacast have at least
     one occurence in the left pattern pat *)
  let tacmetas = [] in
    match pat with
    | Some (patmetas,pat) ->
	(match (list_subtract tacmetas patmetas) with
	| i::_ ->
	    errorlabstrm "add_extern"
	      (str "The meta-variable ?" ++ Ppconstr.pr_patvar i ++ str" is not bound.")
	| []  ->
	    Lib.add_anonymous_leaf
	      (inAutoHint(local,dbname, AddHints [make_extern pri (Some pat) tacast])))
    | None ->
	Lib.add_anonymous_leaf
	  (inAutoHint(local,dbname, AddHints [make_extern pri None tacast]))

let add_externs pri pat tacast local dbnames =
  List.iter (add_extern pri pat tacast local) dbnames

let add_trivials env sigma l local dbnames =
  List.iter
    (fun dbname ->
       Lib.add_anonymous_leaf (
	 inAutoHint(local,dbname, 
		    AddHints (List.map (fun (name, c) -> make_trivial env sigma ~name c) l))))
    dbnames

let forward_intern_tac =
  ref (fun _ -> failwith "intern_tac is not installed for auto")

let set_extern_intern_tac f = forward_intern_tac := f

type hints_entry =
  | HintsResolveEntry of (int option * bool * hints_path_atom * constr) list
  | HintsImmediateEntry of (hints_path_atom * constr) list
  | HintsCutEntry of hints_path
  | HintsUnfoldEntry of evaluable_global_reference list
  | HintsTransparencyEntry of evaluable_global_reference list * bool
  | HintsExternEntry of
      int * (patvar list * constr_pattern) option * glob_tactic_expr

let h = id_of_string "H"

exception Found of constr * types

let prepare_hint env (sigma,c) =
  let sigma = Typeclasses.resolve_typeclasses ~fail:false env sigma in
  (* We re-abstract over uninstantiated evars.
     It is actually a bit stupid to generalize over evars since the first
     thing make_resolves will do is to re-instantiate the products *)
  let c = drop_extra_implicit_args (Evarutil.nf_evar sigma c) in
  let vars = ref (collect_vars c) in
  let subst = ref [] in
  let rec find_next_evar c = match kind_of_term c with
    | Evar (evk,args as ev) ->
      (* We skip the test whether args is the identity or not *)
      let t = Evarutil.nf_evar sigma (existential_type sigma ev) in
      let t = List.fold_right (fun (e,id) c -> replace_term e id c) !subst t in
      if free_rels t <> Intset.empty then
	error "Hints with holes dependent on a bound variable not supported.";
      if occur_existential t then
	(* Not clever enough to construct dependency graph of evars *)
	error "Not clever enough to deal with evars dependent in other evars.";
      raise (Found (c,t))
    | _ -> iter_constr find_next_evar c in
  let rec iter c =
    try find_next_evar c; c
    with Found (evar,t) ->
      let id = next_ident_away_from h (fun id -> Idset.mem id !vars) in
      vars := Idset.add id !vars;
      subst := (evar,mkVar id)::!subst;
      mkNamedLambda id t (iter (replace_term evar (mkVar id) c)) in
  iter c

let path_of_constr_expr c =
  match c with
  | Topconstr.CRef r -> (try PathHints [global r] with _ -> PathAny)
  | _ -> PathAny
      
let interp_hints h =
  let f c =
    let evd,c = Constrintern.interp_open_constr Evd.empty (Global.env()) c in
    let c = prepare_hint (Global.env()) (evd,c) in
    Evarutil.check_evars (Global.env()) Evd.empty evd c;
    c in
  let fr r =
    let gr = global_with_alias r in
    let r' = evaluable_of_global_reference (Global.env()) gr in
    Dumpglob.add_glob (loc_of_reference r) gr;
    r' in
  let fres (o, b, c) = (o, b, path_of_constr_expr c, f c) in
  let fi c = path_of_constr_expr c, f c in
  let fp = Constrintern.intern_constr_pattern Evd.empty (Global.env()) in
  match h with
  | HintsResolve lhints -> HintsResolveEntry (List.map fres lhints)
  | HintsImmediate lhints -> HintsImmediateEntry (List.map fi lhints)
  | HintsUnfold lhints -> HintsUnfoldEntry (List.map fr lhints)
  | HintsTransparency (lhints, b) ->
      HintsTransparencyEntry (List.map fr lhints, b)
  | HintsConstructors lqid ->
      let constr_hints_of_ind qid =
        let ind = global_inductive_with_alias qid in
        list_tabulate (fun i -> let c = (ind,i+1) in
			 None, true, PathHints [ConstructRef c], mkConstruct c)
	  (nconstructors ind) in
	HintsResolveEntry (List.flatten (List.map constr_hints_of_ind lqid))
  | HintsExtern (pri, patcom, tacexp) ->
      let pat =	Option.map fp patcom in
      let tacexp = !forward_intern_tac (match pat with None -> [] | Some (l, _) -> l) tacexp in
      HintsExternEntry (pri, pat, tacexp)

let add_hints local dbnames0 h =
  if List.mem "nocore" dbnames0 then
    error "The hint database \"nocore\" is meant to stay empty.";
  let dbnames = if dbnames0 = [] then ["core"] else dbnames0 in
  let env = Global.env() and sigma = Evd.empty in
  match h with
  | HintsResolveEntry lhints -> add_resolves env sigma lhints local dbnames
  | HintsImmediateEntry lhints -> add_trivials env sigma lhints local dbnames
  | HintsCutEntry lhints -> add_cuts lhints local dbnames
  | HintsUnfoldEntry lhints -> add_unfolds lhints local dbnames
  | HintsTransparencyEntry (lhints, b) ->
      add_transparency lhints b local dbnames
  | HintsExternEntry (pri, pat, tacexp) ->
      add_externs pri pat tacexp local dbnames

(**************************************************************************)
(*                    Functions for printing the hints                    *)
(**************************************************************************)

let pr_autotactic =
  function
  | Res_pf (c,clenv) -> (str"apply " ++ pr_constr c)
  | ERes_pf (c,clenv) -> (str"eapply " ++ pr_constr c)
  | Give_exact c -> (str"exact " ++ pr_constr c)
  | Res_pf_THEN_trivial_fail (c,clenv) ->
      (str"apply " ++ pr_constr c ++ str" ; trivial")
  | Unfold_nth c -> (str"unfold " ++  pr_evaluable_reference c)
  | Extern tac ->
      (str "(*external*) " ++ Pptactic.pr_glob_tactic (Global.env()) tac)

let pr_hint (id, v) =
  (pr_autotactic v.code ++ str"(level " ++ int v.pri ++ str", id " ++ int id ++ str ")" ++ spc ())

let pr_hint_list hintlist =
  (str "  " ++ hov 0 (prlist pr_hint hintlist) ++ fnl ())

let pr_hints_db (name,db,hintlist) =
  (str "In the database " ++ str name ++ str ":" ++
     if hintlist = [] then (str " nothing" ++ fnl ())
     else (fnl () ++ pr_hint_list hintlist))

(* Print all hints associated to head c in any database *)
let pr_hint_list_for_head c =
  let dbs = Hintdbmap.to_list !searchtable in
  let valid_dbs =
    map_succeed
      (fun (name,db) -> (name,db, List.map (fun v -> 0, v) (Hint_db.map_all c db)))
      dbs
  in
  if valid_dbs = [] then
    (str "No hint declared for :" ++ pr_global c)
  else
    hov 0
      (str"For " ++ pr_global c ++ str" -> " ++ fnl () ++
	 hov 0 (prlist pr_hints_db valid_dbs))

let pr_hint_ref ref = pr_hint_list_for_head ref

(* Print all hints associated to head id in any database *)
let print_hint_ref ref =  ppnl(pr_hint_ref ref)

let pr_hint_term cl =
  try
    let dbs = Hintdbmap.to_list !searchtable in
    let valid_dbs =
      let fn = try
	  let (hdc,args) = head_constr_bound cl in
	  let hd = head_of_constr_reference hdc in
	    if occur_existential cl then
	      Hint_db.map_all hd
	    else Hint_db.map_auto (hd, applist (hdc,args))
	with Bound -> Hint_db.map_none
      in
      let fn db = List.map (fun x -> 0, x) (fn db) in
	map_succeed (fun (name, db) -> (name, db, fn db)) dbs
    in
      if valid_dbs = [] then
	(str "No hint applicable for current goal")
      else
	(str "Applicable Hints :" ++ fnl () ++
	    hov 0 (prlist pr_hints_db valid_dbs))
  with Match_failure _ | Failure _ ->
    (str "No hint applicable for current goal")

let error_no_such_hint_database x =
  error ("No such Hint database: "^x^".")

let print_hint_term cl = ppnl (pr_hint_term cl)

(* print all hints that apply to the concl of the current goal *)
let print_applicable_hint () =
  let pts = get_pftreestate () in
  let glss = Proof.V82.subgoals pts in
  match glss.Evd.it with
  | [] -> Util.error "No focused goal."
  | g::_ ->
    let gl = { Evd.it = g; sigma = glss.Evd.sigma } in
    print_hint_term (pf_concl gl)

(* displays the whole hint database db *)
let print_hint_db db =
  let (ids, csts) = Hint_db.transparent_state db in
  msgnl (hov 0
	  ((if Hint_db.use_dn db then str"Discriminated database"
	    else str"Non-discriminated database")));
  msgnl (hov 2 (str"Unfoldable variable definitions: " ++ pr_idpred ids));
  msgnl (hov 2 (str"Unfoldable constant definitions: " ++ pr_cpred csts));
  msgnl (hov 2 (str"Cut: " ++ pp_hints_path (Hint_db.cut db)));
  Hint_db.iter
    (fun head hintlist ->
      match head with
      | Some head ->
	  msg (hov 0
		  (str "For " ++ pr_global head ++ str " -> " ++
		      pr_hint_list (List.map (fun x -> (0,x)) hintlist)))
      | None ->
	  msg (hov 0
		  (str "For any goal -> " ++
		      pr_hint_list (List.map (fun x -> (0, x)) hintlist))))
    db

let print_hint_db_by_name dbname =
  try
    let db = searchtable_map dbname in print_hint_db db
  with Not_found ->
    error_no_such_hint_database dbname

(* displays all the hints of all databases *)
let print_searchtable () =
  Hintdbmap.iter
    (fun name db ->
       msg (str "In the database " ++ str name ++ str ":" ++ fnl ());
       print_hint_db db)
    !searchtable

(**************************************************************************)
(*                           Automatic tactics                            *)
(**************************************************************************)

(**************************************************************************)
(*          tactics with a trace mechanism for automatic search           *)
(**************************************************************************)

let priority l = List.filter (fun (_, hint) -> hint.pri = 0) l

(* tell auto not to reuse already instantiated metas in unification (for
   compatibility, since otherwise, apply succeeds oftener) *)

open Unification

let auto_unif_flags = {
  modulo_conv_on_closed_terms = Some full_transparent_state;
  use_metas_eagerly_in_conv_on_closed_terms = false;
  modulo_delta = empty_transparent_state;
  modulo_delta_types = full_transparent_state;
  check_applied_meta_types = false;
  resolve_evars = true;
  use_pattern_unification = false;
  use_meta_bound_pattern_unification = true;
  frozen_evars = ExistentialSet.empty;
  restrict_conv_on_strict_subterms = false; (* Compat *)
  modulo_betaiota = false;
  modulo_eta = true;
  allow_K_in_toplevel_higher_order_unification = false
}

(* Try unification with the precompiled clause, then use registered Apply *)

let h_clenv_refine ev c clenv =
  Refiner.abstract_tactic (TacApply (true,ev,[c,NoBindings],None))
    (Clenvtac.clenv_refine ev clenv)

let unify_resolve_nodelta (c,clenv) gl =
  let clenv' = connect_clenv gl clenv in
  let clenv'' = clenv_unique_resolver ~flags:auto_unif_flags clenv' gl in
  h_clenv_refine false c clenv'' gl

let unify_resolve flags (c,clenv) gl =
  let clenv' = connect_clenv gl clenv in
  let clenv'' = clenv_unique_resolver ~flags clenv' gl in
  h_clenv_refine false c clenv'' gl

let unify_resolve_gen = function
  | None -> unify_resolve_nodelta
  | Some flags -> unify_resolve flags

(* Util *)

let expand_constructor_hints env lems =
  list_map_append (fun (sigma,lem) ->
    match kind_of_term lem with
    | Ind ind ->
	list_tabulate (fun i -> mkConstruct (ind,i+1)) (nconstructors ind)
    | _ ->
	[prepare_hint env (sigma,lem)]) lems

(* builds a hint database from a constr signature *)
(* typically used with (lid, ltyp) = pf_hyps_types <some goal> *)

let add_hint_lemmas eapply lems hint_db gl =
  let lems = expand_constructor_hints (pf_env gl) lems in
  let hintlist' =
    list_map_append (pf_apply make_resolves gl (eapply,true,false) None) lems in
  Hint_db.add_list hintlist' hint_db

let make_local_hint_db ?ts eapply lems gl =
  let sign = pf_hyps gl in
  let ts = match ts with
    | None -> Hint_db.transparent_state (searchtable_map "core") 
    | Some ts -> ts
  in
  let hintlist = list_map_append (pf_apply make_resolve_hyp gl) sign in
  add_hint_lemmas eapply lems
    (Hint_db.add_list hintlist (Hint_db.empty ts false)) gl

(* Serait-ce possible de compiler d'abord la tactique puis de faire la
   substitution sans passer par bdize dont l'objectif est de préparer un
   terme pour l'affichage ? (HH) *)

(* Si on enlève le dernier argument (gl) conclPattern est calculé une
fois pour toutes : en particulier si Pattern.somatch produit une UserError
Ce qui fait que si la conclusion ne matche pas le pattern, Auto échoue, même
si après Intros la conclusion matche le pattern.
*)

(* conclPattern doit échouer avec error car il est rattraper par tclFIRST *)

let forward_interp_tactic =
  ref (fun _ -> failwith "interp_tactic is not installed for auto")

let set_extern_interp f = forward_interp_tactic := f

let conclPattern concl pat tac gl =
  let constr_bindings =
    match pat with
    | None -> []
    | Some pat ->
	try matches pat concl
	with PatternMatchingFailure -> error "conclPattern" in
    !forward_interp_tactic constr_bindings tac gl

(***********************************************************)
(** A debugging / verbosity framework for trivial and auto *)
(***********************************************************)

(** The following options allow to trigger debugging/verbosity
    without having to adapt the scripts.
    Note: if Debug and Info are both activated, Debug take precedence. *)

let global_debug_trivial = ref false
let global_debug_auto = ref false
let global_info_trivial = ref false
let global_info_auto = ref false

let add_option ls refe =
  let _ = Goptions.declare_bool_option
    { Goptions.optsync  = true;
      Goptions.optdepr  = false;
      Goptions.optname  = String.concat " " ls;
      Goptions.optkey   = ls;
      Goptions.optread  = (fun () -> !refe);
      Goptions.optwrite = (:=) refe }
  in ()

let _ =
  add_option ["Debug";"Trivial"] global_debug_trivial;
  add_option ["Debug";"Auto"] global_debug_auto;
  add_option ["Info";"Trivial"] global_info_trivial;
  add_option ["Info";"Auto"] global_info_auto

let no_dbg () = (Off,0,ref [])

let mk_trivial_dbg debug =
  let d =
    if debug = Debug || !global_debug_trivial then Debug
    else if debug = Info || !global_info_trivial then Info
    else Off
  in (d,0,ref [])

(** Note : we start the debug depth of auto at 1 to distinguish it
   for trivial (whose depth is 0). *)

let mk_auto_dbg debug =
  let d =
    if debug = Debug || !global_debug_auto then Debug
    else if debug = Info || !global_info_auto then Info
    else Off
  in (d,1,ref [])

let incr_dbg = function (dbg,depth,trace) -> (dbg,depth+1,trace)

(** A tracing tactic for debug/info trivial/auto *)

let tclLOG (dbg,depth,trace) pp tac =
  match dbg with
    | Off -> tac
    | Debug ->
       (* For "debug (trivial/auto)", we directly output messages *)
      let s = String.make depth '*' in
      begin fun gl ->
	try
	  let out = tac gl in
	  msg_debug (str s ++ spc () ++ pp () ++ str ". (*success*)");
	  out
	with e ->
	  msg_debug (str s ++ spc () ++ pp () ++ str ". (*fail*)");
	  raise e
      end
    | Info ->
      (* For "info (trivial/auto)", we store a log trace *)
      begin fun gl ->
	try
	  let out = tac gl in
	  trace := (depth, Some pp) :: !trace;
	  out
	with e ->
	  trace := (depth, None) :: !trace;
	  raise e
      end

(** For info, from the linear trace information, we reconstitute the part
    of the proof tree we're interested in. The last executed tactic
    comes first in the trace (and it should be a successful one).
    [depth] is the root depth of the tree fragment we're visiting.
    [keep] means we're in a successful tree fragment (the very last
    tactic has been successful). *)

let rec cleanup_info_trace depth acc = function
  | [] -> acc
  | (d,Some pp) :: l -> cleanup_info_trace d ((d,pp)::acc) l
  | l -> cleanup_info_trace depth acc (erase_subtree depth l)

and erase_subtree depth = function
  | [] -> []
  | (d,_) :: l -> if d = depth then l else erase_subtree depth l

let pr_info_atom (d,pp) =
  msg_debug (str (String.make d ' ') ++ pp () ++ str ".")

let pr_info_trace = function
  | (Info,_,{contents=(d,Some pp)::l}) ->
      List.iter pr_info_atom (cleanup_info_trace d [(d,pp)] l)
  | _ -> ()

let pr_info_nop = function
  | (Info,_,_) -> msg_debug (str "idtac.")
  | _ -> ()

let pr_dbg_header = function
  | (Off,_,_) -> ()
  | (Debug,0,_) -> msg_debug (str "(* debug trivial : *)")
  | (Debug,_,_) -> msg_debug (str "(* debug auto : *)")
  | (Info,0,_) -> msg_debug (str "(* info trivial : *)")
  | (Info,_,_) -> msg_debug (str "(* info auto : *)")

let tclTRY_dbg d tac =
  tclORELSE0
    (fun gl ->
      pr_dbg_header d;
      let out = tac gl in
      pr_info_trace d;
      out)
    (fun gl ->
      pr_info_nop d;
      tclIDTAC gl)

(**************************************************************************)
(*                           The Trivial tactic                           *)
(**************************************************************************)

(* local_db is a Hint database containing the hypotheses of current goal *)
(* Papageno : cette fonction a été pas mal simplifiée depuis que la base
  de Hint impérative a été remplacée par plusieurs bases fonctionnelles *)

let flags_of_state st =
  {auto_unif_flags with
    modulo_conv_on_closed_terms = Some st; modulo_delta = st}

let hintmap_of hdc concl =
  match hdc with
  | None -> Hint_db.map_none
  | Some hdc ->
      if occur_existential concl then Hint_db.map_all hdc
      else Hint_db.map_auto (hdc,concl)

let exists_evaluable_reference env = function
  | EvalConstRef _ -> true
  | EvalVarRef v -> try ignore(lookup_named v env); true with Not_found -> false

let dbg_intro dbg = tclLOG dbg (fun () -> str "intro") intro
let dbg_assumption dbg = tclLOG dbg (fun () -> str "assumption") assumption

let rec trivial_fail_db dbg mod_delta db_list local_db gl =
  let intro_tac =
    tclTHEN (dbg_intro dbg)
      (fun g'->
	 let hintl = make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
	 in trivial_fail_db dbg mod_delta db_list (Hint_db.add_list hintl local_db) g')
  in
  tclFIRST
    ((dbg_assumption dbg)::intro_tac::
     (List.map tclCOMPLETE
       (trivial_resolve dbg mod_delta db_list local_db (pf_concl gl)))) gl

and my_find_search_nodelta db_list local_db hdc concl =
  List.map (fun hint -> (None,hint))
    (list_map_append (hintmap_of hdc concl) (local_db::db_list))

and my_find_search mod_delta =
  if mod_delta then my_find_search_delta
  else my_find_search_nodelta

and my_find_search_delta db_list local_db hdc concl =
  let flags = {auto_unif_flags with use_metas_eagerly_in_conv_on_closed_terms = true} in
  let f = hintmap_of hdc concl in
    if occur_existential concl then
      list_map_append
	(fun db ->
	  if Hint_db.use_dn db then
	    let flags = flags_of_state (Hint_db.transparent_state db) in
	      List.map (fun x -> (Some flags,x)) (f db)
	  else
	    let flags = {flags with modulo_delta = Hint_db.transparent_state db} in
	      List.map (fun x -> (Some flags,x)) (f db))
	(local_db::db_list)
    else
      list_map_append (fun db ->
	if Hint_db.use_dn db then
	  let flags = flags_of_state (Hint_db.transparent_state db) in
	    List.map (fun x -> (Some flags, x)) (f db)
	else
	  let (ids, csts as st) = Hint_db.transparent_state db in
	  let flags, l =
	    let l =
	      match hdc with None -> Hint_db.map_none db
	      | Some hdc ->
		  if (Idpred.is_empty ids && Cpred.is_empty csts)
		  then Hint_db.map_auto (hdc,concl) db
		  else Hint_db.map_all hdc db
	    in {flags with modulo_delta = st}, l
	  in List.map (fun x -> (Some flags,x)) l)
      	(local_db::db_list)

and tac_of_hint dbg db_list local_db concl (flags, ({pat=p; code=t})) =
  let tactic = 
    match t with
    | Res_pf (c,cl) -> unify_resolve_gen flags (c,cl)
    | ERes_pf _ -> (fun gl -> error "eres_pf")
    | Give_exact c  -> exact_check c
    | Res_pf_THEN_trivial_fail (c,cl) ->
      tclTHEN
        (unify_resolve_gen flags (c,cl))
	(* With "(debug) trivial", we shouldn't end here, and
	   with "debug auto" we don't display the details of inner trivial *)
        (trivial_fail_db (no_dbg ()) (flags <> None) db_list local_db)
    | Unfold_nth c ->
      (fun gl ->
       if exists_evaluable_reference (pf_env gl) c then
	 tclPROGRESS (h_reduce (Unfold [all_occurrences_expr,c]) onConcl) gl
       else tclFAIL 0 (str"Unbound reference") gl)
    | Extern tacast -> conclPattern concl p tacast
  in
  tclLOG dbg (fun () -> pr_autotactic t) tactic

and trivial_resolve dbg mod_delta db_list local_db cl =
  try
    let head =
      try let hdconstr,_ = head_constr_bound cl in
	    Some (head_of_constr_reference hdconstr)
      with Bound -> None
    in
      List.map (tac_of_hint dbg db_list local_db cl)
	(priority
	    (my_find_search mod_delta db_list local_db head cl))
  with Not_found -> []

(** The use of the "core" database can be de-activated by passing
    "nocore" amongst the databases. *)

let make_db_list dbnames =
  let use_core = not (List.mem "nocore" dbnames) in
  let dbnames = list_remove "nocore" dbnames in
  let dbnames = if use_core then "core"::dbnames else dbnames in
  let lookup db =
    try searchtable_map db with Not_found -> error_no_such_hint_database db
  in
  List.map lookup dbnames

let trivial ?(debug=Off) lems dbnames gl =
  let db_list = make_db_list dbnames in
  let d = mk_trivial_dbg debug in
  tclTRY_dbg d
    (trivial_fail_db d false db_list (make_local_hint_db false lems gl)) gl

let full_trivial ?(debug=Off) lems gl =
  let dbnames = Hintdbmap.dom !searchtable in
  let dbnames = list_remove "v62" dbnames in
  let db_list = List.map (fun x -> searchtable_map x) dbnames in
  let d = mk_trivial_dbg debug in
  tclTRY_dbg d
    (trivial_fail_db d false db_list (make_local_hint_db false lems gl)) gl

let gen_trivial ?(debug=Off) lems = function
  | None -> full_trivial ~debug lems
  | Some l -> trivial ~debug lems l

let h_trivial ?(debug=Off) lems l =
  Refiner.abstract_tactic (TacTrivial (debug,List.map snd lems,l))
    (gen_trivial ~debug lems l)

(**************************************************************************)
(*                       The classical Auto tactic                        *)
(**************************************************************************)

let possible_resolve dbg mod_delta db_list local_db cl =
  try
    let head =
      try let hdconstr,_ = head_constr_bound cl in
	    Some (head_of_constr_reference hdconstr)
      with Bound -> None
    in
      List.map (tac_of_hint dbg db_list local_db cl)
	(my_find_search mod_delta db_list local_db head cl)
  with Not_found -> []

let dbg_case dbg id =
  tclLOG dbg (fun () -> str "case " ++ pr_id id) (simplest_case (mkVar id))

let decomp_unary_term_then dbg (id,_,typc) kont1 kont2 gl =
  try
    let ccl = applist (head_constr typc) in
    match Hipattern.match_with_conjunction ccl with
    | Some (_,args) ->
	tclTHEN (dbg_case dbg id) (kont1 (List.length args)) gl
    | None ->
	kont2 gl
  with UserError _ -> kont2 gl

let decomp_empty_term dbg (id,_,typc) gl =
  if Hipattern.is_empty_type typc then
    dbg_case dbg id gl
  else
    errorlabstrm "Auto.decomp_empty_term" (str "Not an empty type.")

let extend_local_db gl decl db =
  Hint_db.add_list (make_resolve_hyp (pf_env gl) (project gl) decl) db

(* Introduce an hypothesis, then call the continuation tactic [kont]
   with the hint db extended with the so-obtained hypothesis *)

let intro_register dbg kont db =
  tclTHEN (dbg_intro dbg)
    (onLastDecl (fun decl gl -> kont (extend_local_db gl decl db) gl))

(* n is the max depth of search *)
(* local_db contains the local Hypotheses *)

exception Uplift of tactic list

let search d n mod_delta db_list local_db =
  let rec search d n local_db =
    if n=0 then (fun gl -> error "BOUND 2") else
      tclORELSE0 (dbg_assumption d)
	(tclORELSE0 (intro_register d (search d n) local_db)
	   (fun gl ->
	     let d' = incr_dbg d in
	     tclFIRST
	       (List.map
		  (fun ntac -> tclTHEN ntac (search d' (n-1) local_db))
		  (possible_resolve d mod_delta db_list local_db (pf_concl gl))) gl))
  in
  search d n local_db

let default_search_depth = ref 5

let delta_auto ?(debug=Off) mod_delta n lems dbnames gl =
  let db_list = make_db_list dbnames in
  let d = mk_auto_dbg debug in
  tclTRY_dbg d
    (search d n mod_delta db_list (make_local_hint_db false lems gl)) gl

let auto ?(debug=Off) n = delta_auto ~debug false n

let new_auto ?(debug=Off) n = delta_auto ~debug true n

let default_auto = auto !default_search_depth [] []

let delta_full_auto ?(debug=Off) mod_delta n lems gl =
  let dbnames = Hintdbmap.dom !searchtable in
  let dbnames = list_remove "v62" dbnames in
  let db_list = List.map (fun x -> searchtable_map x) dbnames in
  let d = mk_auto_dbg debug in
  tclTRY_dbg d
    (search d n mod_delta db_list (make_local_hint_db false lems gl)) gl

let full_auto ?(debug=Off) n = delta_full_auto ~debug false n
let new_full_auto ?(debug=Off) n = delta_full_auto ~debug true n

let default_full_auto gl = full_auto !default_search_depth [] gl

let gen_auto ?(debug=Off) n lems dbnames =
  let n = match n with None -> !default_search_depth | Some n -> n in
  match dbnames with
  | None -> full_auto ~debug n lems
  | Some l -> auto ~debug n lems l

let inj_or_var = Option.map (fun n -> ArgArg n)

let h_auto ?(debug=Off) n lems l =
  Refiner.abstract_tactic (TacAuto (debug,inj_or_var n,List.map snd lems,l))
    (gen_auto ~debug n lems l)