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(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2019       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Pp
open CErrors
open Util
open Names
open Constr
open Termops
open EConstr
open Tacticals
open Tacmach
open Evd
open Tactics
open Clenv
open Auto
open Genredexpr
open Tactypes
open Locus
open Locusops
open Hints
open Proofview.Notations

let eauto_unif_flags = auto_flags_of_state TransparentState.full

let e_give_exact ?(flags=eauto_unif_flags) c =
  Proofview.Goal.enter begin fun gl ->
  let t1 = Tacmach.New.pf_unsafe_type_of gl c in
  let t2 = Tacmach.New.pf_concl gl in
  let sigma = Tacmach.New.project gl in
  if occur_existential sigma t1 || occur_existential sigma t2 then
     Tacticals.New.tclTHEN (Clenvtac.unify ~flags t1) (exact_no_check c)
  else exact_check c
  end

let assumption id = e_give_exact (mkVar id)

let e_assumption =
  Proofview.Goal.enter begin fun gl ->
    Tacticals.New.tclFIRST (List.map assumption (Tacmach.New.pf_ids_of_hyps gl))
  end

let registered_e_assumption =
  Proofview.Goal.enter begin fun gl ->
  Tacticals.New.tclFIRST (List.map (fun id -> e_give_exact (mkVar id))
              (Tacmach.New.pf_ids_of_hyps gl))
  end

(************************************************************************)
(*   PROLOG tactic                                                      *)
(************************************************************************)

(*s Tactics handling a list of goals. *)

(* first_goal : goal list sigma -> goal sigma *)

let first_goal gls =
  let gl = gls.Evd.it and sig_0 = gls.Evd.sigma in
  if List.is_empty gl then user_err Pp.(str "first_goal");
  { Evd.it = List.hd gl; Evd.sigma = sig_0; }

(* tactic -> tactic_list : Apply a tactic to the first goal in the list *)

let apply_tac_list tac glls =
  match glls.it with
  | (g1::rest) ->
      let pack = tac (re_sig g1 glls.sigma) in
      re_sig (pack.it @ rest) pack.sigma
  | _ -> user_err Pp.(str "apply_tac_list")

let one_step l gl =
  [Proofview.V82.of_tactic Tactics.intro]
  @ (List.map (fun c -> Proofview.V82.of_tactic (Tactics.Simple.eapply c)) (List.map mkVar (pf_ids_of_hyps gl)))
  @ (List.map (fun c -> Proofview.V82.of_tactic (Tactics.Simple.eapply c)) l)
  @ (List.map (fun c -> Proofview.V82.of_tactic (assumption c)) (pf_ids_of_hyps gl))

let rec prolog l n gl =
  if n <= 0 then user_err Pp.(str "prolog - failure");
  let prol = (prolog l (n-1)) in
  (tclFIRST (List.map (fun t -> (tclTHEN t prol)) (one_step l gl))) gl

let out_term env = function
  | IsConstr (c, _) -> c
  | IsGlobRef gr -> EConstr.of_constr (fst (UnivGen.fresh_global_instance env gr))

let prolog_tac l n =
  Proofview.V82.tactic begin fun gl ->
  let map c =
    let (sigma, c) = c (pf_env gl) (project gl) in
    let c = pf_apply (prepare_hint false (false,true)) gl (sigma, c) in
    out_term (pf_env gl) c
  in
  let l = List.map map l in
  try (prolog l n gl)
  with UserError (Some "Refiner.tclFIRST",_) ->
    user_err ~hdr:"Prolog.prolog" (str "Prolog failed.")
  end

open Auto

(***************************************************************************)
(* A tactic similar to Auto, but using EApply, Assumption and e_give_exact *)
(***************************************************************************)

let priority l = List.map snd (List.filter (fun (pr,_) -> Int.equal pr 0) l)

let unify_e_resolve poly flags (c,clenv) =
  Proofview.Goal.enter begin fun gl ->
      let clenv', c = connect_hint_clenv ~poly c clenv gl in
      let clenv' = clenv_unique_resolver ~flags clenv' gl in
      Proofview.tclTHEN
        (Proofview.Unsafe.tclEVARUNIVCONTEXT (Evd.evar_universe_context clenv'.evd))
        (Tactics.Simple.eapply c)
    end

let hintmap_of sigma secvars hdc concl =
  match hdc with
  | None -> fun db -> Hint_db.map_none ~secvars db
  | Some hdc ->
     if occur_existential sigma concl then
       (fun db -> Hint_db.map_existential sigma ~secvars hdc concl db)
     else (fun db -> Hint_db.map_auto sigma ~secvars hdc concl db)
   (* FIXME: should be (Hint_db.map_eauto hdc concl db) *)

let e_exact poly flags (c,clenv) =
  Proofview.Goal.enter begin fun gl ->
    let clenv', c = connect_hint_clenv ~poly c clenv gl in
    Tacticals.New.tclTHEN
    (Proofview.Unsafe.tclEVARUNIVCONTEXT (Evd.evar_universe_context clenv'.evd))
    (e_give_exact c)
  end

let rec e_trivial_fail_db db_list local_db =
  let next = Proofview.Goal.enter begin fun gl ->
    let d = Tacmach.New.pf_last_hyp gl in
    let hintl = make_resolve_hyp (Tacmach.New.pf_env gl) (Tacmach.New.project gl) d in
    e_trivial_fail_db db_list (Hint_db.add_list (Tacmach.New.pf_env gl) (Tacmach.New.project gl) hintl local_db)
  end in
  Proofview.Goal.enter begin fun gl ->
  let secvars = compute_secvars gl in
  let tacl =
    registered_e_assumption ::
    (Tacticals.New.tclTHEN Tactics.intro next) ::
    (List.map fst (e_trivial_resolve (Tacmach.New.pf_env gl) (Tacmach.New.project gl) db_list local_db secvars (Tacmach.New.pf_concl gl)))
  in
  Tacticals.New.tclSOLVE tacl
  end

and e_my_find_search env sigma db_list local_db secvars hdc concl =
  let hint_of_db = hintmap_of sigma secvars hdc concl in
  let hintl =
      List.map_append (fun db ->
        let flags = auto_flags_of_state (Hint_db.transparent_state db) in
          List.map (fun x -> flags, x) (hint_of_db db)) (local_db::db_list)
  in
  let tac_of_hint =
    fun (st, {pri = b; pat = p; code = t; poly = poly}) ->
      let b = match Hints.repr_hint t with
      | Unfold_nth _ -> 1
      | _ -> b
      in
      (b,
        let tac = function
        | Res_pf (term,cl) -> unify_resolve ~poly st (term,cl)
        | ERes_pf (term,cl) -> unify_e_resolve poly st (term,cl)
        | Give_exact (c,cl) -> e_exact poly st (c,cl)
        | Res_pf_THEN_trivial_fail (term,cl) ->
          Tacticals.New.tclTHEN (unify_e_resolve poly st (term,cl))
            (e_trivial_fail_db db_list local_db)
        | Unfold_nth c -> reduce (Unfold [AllOccurrences,c]) onConcl
        | Extern tacast -> conclPattern concl p tacast
       in
       let tac = run_hint t tac in
       (tac, lazy (pr_hint env sigma t)))
  in
  List.map tac_of_hint hintl

and e_trivial_resolve env sigma db_list local_db secvars gl =
  let hd = try Some (decompose_app_bound sigma gl) with Bound -> None in
  try priority (e_my_find_search env sigma db_list local_db secvars hd gl)
  with Not_found -> []

let e_possible_resolve env sigma db_list local_db secvars gl =
  let hd = try Some (decompose_app_bound sigma gl) with Bound -> None in
  try List.map (fun (b, (tac, pp)) -> (tac, b, pp))
               (e_my_find_search env sigma db_list local_db secvars hd gl)
  with Not_found -> []

let find_first_goal gls =
  try first_goal gls with UserError _ -> assert false

(*s The following module [SearchProblem] is used to instantiate the generic
    exploration functor [Explore.Make]. *)

type search_state = {
  priority : int;
  depth : int; (*r depth of search before failing *)
  tacres : Goal.goal list sigma;
  last_tactic : Pp.t Lazy.t;
  dblist : hint_db list;
  localdb :  hint_db list;
  prev : prev_search_state;
  local_lemmas : delayed_open_constr list;
}

and prev_search_state = (* for info eauto *)
  | Unknown
  | Init
  | State of search_state

module SearchProblem = struct

  type state = search_state

  let success s = List.is_empty (sig_it s.tacres)

(*   let pr_ev evs ev = Printer.pr_constr_env (Evd.evar_env ev) (Evarutil.nf_evar evs ev.Evd.evar_concl) *)

  let filter_tactics glls l =
(*     let _ = Proof_trees.db_pr_goal (List.hd (sig_it glls)) in *)
(*     let evars = Evarutil.nf_evars (Refiner.project glls) in *)
(*     msg (str"Goal:" ++ pr_ev evars (List.hd (sig_it glls)) ++ str"\n"); *)
    let rec aux = function
      | [] -> []
      | (tac, cost, pptac) :: tacl ->
          try
            let lgls = apply_tac_list (Proofview.V82.of_tactic tac) glls in
(*             let gl = Proof_trees.db_pr_goal (List.hd (sig_it glls)) in *)
(*               msg (hov 1 (pptac ++ str" gives: \n" ++ pr_goals lgls ++ str"\n")); *)
              (lgls, cost, pptac) :: aux tacl
          with e when CErrors.noncritical e ->
            let e = CErrors.push e in
            Refiner.catch_failerror e; aux tacl
    in aux l

  (* Ordering of states is lexicographic on depth (greatest first) then
     number of remaining goals. *)
  let compare s s' =
    let d = s'.depth - s.depth in
    let d' = Int.compare s.priority s'.priority in
    let nbgoals s = List.length (sig_it s.tacres) in
    if not (Int.equal d 0) then d
    else if not (Int.equal d' 0) then d'
    else Int.compare (nbgoals s) (nbgoals s')

  let branching s =
    if Int.equal s.depth 0 then
      []
    else
      let ps = if s.prev == Unknown then Unknown else State s in
      let lg = s.tacres in
      let nbgl = List.length (sig_it lg) in
      assert (nbgl > 0);
      let g = find_first_goal lg in
      let hyps = pf_ids_of_hyps g in
      let secvars = secvars_of_hyps (pf_hyps g) in
      let map_assum id = (e_give_exact (mkVar id), (-1), lazy (str "exact" ++ spc () ++ Id.print id)) in
      let assumption_tacs =
        let tacs = List.map map_assum hyps in
        let l = filter_tactics s.tacres tacs in
        List.map (fun (res, cost, pp) -> { depth = s.depth; priority = cost; tacres = res;
                                    last_tactic = pp; dblist = s.dblist;
                                    localdb = List.tl s.localdb;
                                    prev = ps; local_lemmas = s.local_lemmas}) l
      in
      let intro_tac =
        let l = filter_tactics s.tacres [Tactics.intro, (-1), lazy (str "intro")] in
        List.map
          (fun (lgls, cost, pp) ->
             let g' = first_goal lgls in
             let hintl =
               make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
             in
             let ldb = Hint_db.add_list (pf_env g') (project g')
                  hintl (List.hd s.localdb) in
             { depth = s.depth; priority = cost; tacres = lgls;
               last_tactic = pp; dblist = s.dblist;
               localdb = ldb :: List.tl s.localdb; prev = ps;
               local_lemmas = s.local_lemmas})
          l
      in
      let rec_tacs =
        let l =
          let concl = Reductionops.nf_evar (project g) (pf_concl g) in
          filter_tactics s.tacres
                         (e_possible_resolve (pf_env g) (project g) s.dblist (List.hd s.localdb) secvars concl)
        in
        List.map
          (fun (lgls, cost, pp) ->
             let nbgl' = List.length (sig_it lgls) in
             if nbgl' < nbgl then
               { depth = s.depth; priority = cost; tacres = lgls; last_tactic = pp;
                  prev = ps; dblist = s.dblist; localdb = List.tl s.localdb;
                  local_lemmas = s.local_lemmas }
             else
               let newlocal = 
                 let hyps = pf_hyps g in
                   List.map (fun gl ->
                     let gls = {Evd.it = gl; sigma = lgls.Evd.sigma } in
                     let hyps' = pf_hyps gls in
                       if hyps' == hyps then List.hd s.localdb
                       else make_local_hint_db (pf_env gls) (project gls) ~ts:TransparentState.full true s.local_lemmas)
                     (List.firstn ((nbgl'-nbgl) + 1) (sig_it lgls))
               in
                 { depth = pred s.depth; priority = cost; tacres = lgls;
                   dblist = s.dblist; last_tactic = pp; prev = ps;
                   localdb = newlocal @ List.tl s.localdb;
                   local_lemmas = s.local_lemmas })
          l
      in
      List.sort compare (assumption_tacs @ intro_tac @ rec_tacs)

  let pp s = hov 0 (str " depth=" ++ int s.depth ++ spc () ++
                      (Lazy.force s.last_tactic))

end

module Search = Explore.Make(SearchProblem)

(** Utilities for debug eauto / info eauto *)

let global_debug_eauto = ref false
let global_info_eauto = ref false

let () =
  Goptions.(declare_bool_option
    { optdepr  = false;
      optname  = "Debug Eauto";
      optkey   = ["Debug";"Eauto"];
      optread  = (fun () -> !global_debug_eauto);
      optwrite = (:=) global_debug_eauto })

let () =
  Goptions.(declare_bool_option
    { optdepr  = false;
      optname  = "Info Eauto";
      optkey   = ["Info";"Eauto"];
      optread  = (fun () -> !global_info_eauto);
      optwrite = (:=) global_info_eauto })

let mk_eauto_dbg d =
  if d == Debug || !global_debug_eauto then Debug
  else if d == Info || !global_info_eauto then Info
  else Off

let pr_info_nop = function
  | Info -> Feedback.msg_notice (str "idtac.")
  | _ -> ()

let pr_dbg_header = function
  | Off -> ()
  | Debug -> Feedback.msg_notice (str "(* debug eauto: *)")
  | Info  -> Feedback.msg_notice (str "(* info eauto: *)")

let pr_info dbg s =
  if dbg != Info then ()
  else
    let rec loop s =
      match s.prev with
        | Unknown | Init -> s.depth
        | State sp ->
          let mindepth = loop sp in
          let indent = String.make (mindepth - sp.depth) ' ' in
          Feedback.msg_notice (str indent ++ Lazy.force s.last_tactic ++ str ".");
          mindepth
    in
    ignore (loop s)

(** Eauto main code *)

let make_initial_state dbg n gl dblist localdb lems =
  { depth = n;
    priority = 0;
    tacres = tclIDTAC gl;
    last_tactic = lazy (mt());
    dblist = dblist;
    localdb = [localdb];
    prev = if dbg == Info then Init else Unknown;
    local_lemmas = lems;
  }

let e_search_auto debug (in_depth,p) lems db_list gl =
  let local_db = make_local_hint_db (pf_env gl) (project gl) ~ts:TransparentState.full true lems in
  let d = mk_eauto_dbg debug in
  let tac = match in_depth,d with
    | (true,Debug) -> Search.debug_depth_first
    | (true,_) -> Search.depth_first
    | (false,Debug) -> Search.debug_breadth_first
    | (false,_) -> Search.breadth_first
  in
  try
    pr_dbg_header d;
    let s = tac (make_initial_state d p gl db_list local_db lems) in
    pr_info d s;
    s.tacres
  with Not_found ->
    pr_info_nop d;
    user_err Pp.(str "eauto: search failed")

(* let e_search_auto_key = CProfile.declare_profile "e_search_auto" *)
(* let e_search_auto = CProfile.profile5 e_search_auto_key e_search_auto *)

let eauto_with_bases ?(debug=Off) np lems db_list =
  Hints.wrap_hint_warning (Proofview.V82.tactic (tclTRY (e_search_auto debug np lems db_list)))

let eauto ?(debug=Off) np lems dbnames =
  let db_list = make_db_list dbnames in
  tclTRY (e_search_auto debug np lems db_list)

let full_eauto ?(debug=Off) n lems gl =
  let db_list = current_pure_db () in
  tclTRY (e_search_auto debug n lems db_list) gl

let gen_eauto ?(debug=Off) np lems = function
  | None -> Hints.wrap_hint_warning (Proofview.V82.tactic (full_eauto ~debug np lems))
  | Some l -> Hints.wrap_hint_warning (Proofview.V82.tactic (eauto ~debug np lems l))

let make_depth = function
  | None -> !default_search_depth
  | Some d -> d

let make_dimension n = function
  | None -> (true,make_depth n)
  | Some d -> (false,d)

let cons a l = a :: l

let autounfolds db occs cls gl =
  let unfolds = List.concat (List.map (fun dbname -> 
    let db = try searchtable_map dbname 
      with Not_found -> user_err ~hdr:"autounfold" (str "Unknown database " ++ str dbname)
    in
    let (ids, csts) = Hint_db.unfolds db in
    let hyps = pf_ids_of_hyps gl in
    let ids = Id.Set.filter (fun id -> List.mem id hyps) ids in
      Cset.fold (fun cst -> cons (AllOccurrences, EvalConstRef cst)) csts
        (Id.Set.fold (fun id -> cons (AllOccurrences, EvalVarRef id)) ids [])) db)
  in Proofview.V82.of_tactic (unfold_option unfolds cls) gl

let autounfold db cls =
  Proofview.V82.tactic begin fun gl ->
  let cls = concrete_clause_of (fun () -> pf_ids_of_hyps gl) cls in
  let tac = autounfolds db in
  tclMAP (function
    | OnHyp (id,occs,where) -> tac occs (Some (id,where))
    | OnConcl occs -> tac occs None)
    cls gl
  end

let autounfold_tac db cls =
  Proofview.tclUNIT () >>= fun () ->
  let dbs = match db with
  | None -> String.Set.elements (current_db_names ())
  | Some [] -> ["core"]
  | Some l -> l
  in
  autounfold dbs cls

let unfold_head env sigma (ids, csts) c =
  let rec aux c = 
    match EConstr.kind sigma c with
    | Var id when Id.Set.mem id ids ->
        (match Environ.named_body id env with
        | Some b -> true, EConstr.of_constr b
        | None -> false, c)
    | Const (cst, u) when Cset.mem cst csts ->
        let u = EInstance.kind sigma u in
        true, EConstr.of_constr (Environ.constant_value_in env (cst, u))
    | App (f, args) ->
        (match aux f with
        | true, f' -> true, Reductionops.whd_betaiota sigma (mkApp (f', args))
        | false, _ -> 
            let done_, args' = 
              Array.fold_left_i (fun i (done_, acc) arg -> 
                if done_ then done_, arg :: acc 
                else match aux arg with
                | true, arg' -> true, arg' :: acc
                | false, arg' -> false, arg :: acc)
                (false, []) args
            in 
              if done_ then true, mkApp (f, Array.of_list (List.rev args'))
              else false, c)
    | _ -> 
        let done_ = ref false in
        let c' = EConstr.map sigma (fun c -> 
          if !done_ then c else 
            let x, c' = aux c in
              done_ := x; c') c
        in !done_, c'
  in aux c

let autounfold_one db cl =
  Proofview.Goal.enter begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.New.project gl in
  let concl = Proofview.Goal.concl gl in
  let st =
    List.fold_left (fun (i,c) dbname -> 
      let db = try searchtable_map dbname 
        with Not_found -> user_err ~hdr:"autounfold" (str "Unknown database " ++ str dbname)
      in
      let (ids, csts) = Hint_db.unfolds db in
        (Id.Set.union ids i, Cset.union csts c)) (Id.Set.empty, Cset.empty) db
  in
  let did, c' = unfold_head env sigma st 
    (match cl with Some (id, _) -> Tacmach.New.pf_get_hyp_typ id gl | None -> concl) 
  in
    if did then
      match cl with
      | Some hyp -> change_in_hyp ~check:true None (make_change_arg c') hyp
      | None -> convert_concl ~check:false c' DEFAULTcast
    else Tacticals.New.tclFAIL 0 (str "Nothing to unfold")
  end
tactics/eauto.ml

72.15%
