path: root/tactics/auto.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(*
*)
open Pp
open Util
open CErrors
open Names
open Vars
open Termops
open Environ
open Tacmach
open Genredexpr
open Tactics
open Tacticals
open Clenv
open Tacexpr
open Locus
open Proofview.Notations
open Hints

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

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

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

let compute_secvars gl =
  let hyps = Proofview.Goal.hyps (Proofview.Goal.assume gl) in
  secvars_of_hyps hyps

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

open Unification

let auto_core_unif_flags_of st1 st2 useeager = {
  modulo_conv_on_closed_terms = Some st1;
  use_metas_eagerly_in_conv_on_closed_terms = useeager;
  use_evars_eagerly_in_conv_on_closed_terms = false;
  modulo_delta = st2;
  modulo_delta_types = full_transparent_state;
  check_applied_meta_types = false;
  use_pattern_unification = false;
  use_meta_bound_pattern_unification = true;
  frozen_evars = Evar.Set.empty;
  restrict_conv_on_strict_subterms = false; (* Compat *)
  modulo_betaiota = false;
  modulo_eta = true;
}

let auto_unif_flags_of st1 st2 useeager =
  let flags = auto_core_unif_flags_of st1 st2 useeager in {
  core_unify_flags = flags;
  merge_unify_flags = flags;
  subterm_unify_flags = { flags with modulo_delta = empty_transparent_state };
  allow_K_in_toplevel_higher_order_unification = false;
  resolve_evars = true
}

let auto_unif_flags =
  auto_unif_flags_of full_transparent_state empty_transparent_state false

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

let connect_hint_clenv poly (c, _, ctx) clenv gl =
  (** [clenv] has been generated by a hint-making function, so the only relevant
      data in its evarmap is the set of metas. The [evar_reset_evd] function
      below just replaces the metas of sigma by those coming from the clenv. *)
  let sigma = Tacmach.New.project gl in
  let evd = Evd.evars_reset_evd ~with_conv_pbs:true ~with_univs:false sigma clenv.evd in
  (** Still, we need to update the universes *)
  let clenv, c =
    if poly then
      (** Refresh the instance of the hint *)
      let (subst, ctx) = Universes.fresh_universe_context_set_instance ctx in
      let map c = Vars.subst_univs_level_constr subst c in
      let evd = Evd.merge_context_set Evd.univ_flexible evd ctx in
      (** Only metas are mentioning the old universes. *)
      let clenv = {
        templval = Evd.map_fl map clenv.templval;
        templtyp = Evd.map_fl map clenv.templtyp;
        evd = Evd.map_metas map evd;
        env = Proofview.Goal.env gl;
      } in
      clenv, map c
    else
      let evd = Evd.merge_context_set Evd.univ_flexible evd ctx in
      { clenv with evd = evd ; env = Proofview.Goal.env gl }, c
  in clenv, c

let unify_resolve poly flags ((c : raw_hint), clenv) =
  Proofview.Goal.nf_enter { enter = begin fun gl ->
  let clenv, c = connect_hint_clenv poly c clenv gl in
  let clenv = Tacmach.New.of_old (fun gl -> clenv_unique_resolver ~flags clenv gl) gl in
  Clenvtac.clenv_refine false clenv
  end }

let unify_resolve_nodelta poly h = unify_resolve poly auto_unif_flags h

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

let exact poly (c,clenv) =
  Proofview.Goal.enter { 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))
    (exact_check c)
  end }

(* Util *)

(* 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 conclPattern concl pat tac =
  let constr_bindings env sigma =
    match pat with
    | None -> Proofview.tclUNIT Id.Map.empty
    | Some pat ->
	try
	  Proofview.tclUNIT (Constr_matching.matches env sigma pat concl)
	with Constr_matching.PatternMatchingFailure ->
          Tacticals.New.tclZEROMSG (str "conclPattern")
  in
  Proofview.Goal.enter { enter = begin fun gl ->
     let env = Proofview.Goal.env gl in
     let sigma = Tacmach.New.project gl in
       constr_bindings env sigma >>= fun constr_bindings ->
     let open Genarg in
     let open Geninterp in
     let inj c = match val_tag (topwit Constrarg.wit_constr) with
     | Val.Base tag -> Val.Dyn (tag, c)
     | _ -> assert false
     in
     let fold id c accu = Id.Map.add id (inj c) accu in
     let lfun = Id.Map.fold fold constr_bindings Id.Map.empty in
     let ist = { lfun; extra = TacStore.empty } in
     match tac with
     | GenArg (Glbwit wit, tac) ->
      Ftactic.run (Geninterp.interp wit ist tac) (fun _ -> Proofview.tclUNIT ())
  end }

(***********************************************************)
(** 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
      Proofview.V82.tactic begin fun gl ->
	try
	  let out = Proofview.V82.of_tactic tac gl in
	  Feedback.msg_debug (str s ++ spc () ++ pp () ++ str ". (*success*)");
	  out
	with reraise ->
          let reraise = CErrors.push reraise in
	  Feedback.msg_debug (str s ++ spc () ++ pp () ++ str ". (*fail*)");
	  iraise reraise
      end
    | Info ->
      (* For "info (trivial/auto)", we store a log trace *)
      Proofview.V82.tactic begin fun gl ->
	try
	  let out = Proofview.V82.of_tactic tac gl in
	  trace := (depth, Some pp) :: !trace;
	  out
	with reraise ->
          let reraise = CErrors.push reraise in
	  trace := (depth, None) :: !trace;
	  iraise reraise
      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 Int.equal d depth then l else erase_subtree depth l

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

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

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

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

let tclTRY_dbg d tac =
  let delay f = Proofview.tclUNIT () >>= fun () -> f () in
  let tac = delay (fun () -> pr_dbg_header d; tac) >>=
              fun () -> pr_info_trace d; Proofview.tclUNIT () in
  let after = delay (fun () -> pr_info_nop d; Proofview.tclUNIT ()) in
  Tacticals.New.tclORELSE0 tac after

(**************************************************************************)
(*                           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_of st st false

let auto_flags_of_state st =
  auto_unif_flags_of full_transparent_state st false

let hintmap_of secvars hdc concl =
  match hdc with
  | None -> Hint_db.map_none ~secvars
  | Some hdc ->
     if occur_existential concl then
       Hint_db.map_existential ~secvars hdc concl
     else Hint_db.map_auto ~secvars 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 =
  let intro_tac =
    Tacticals.New.tclTHEN (dbg_intro dbg)
      ( Proofview.Goal.enter { enter = begin fun gl ->
          let sigma = Tacmach.New.project gl in
          let env = Proofview.Goal.env gl in
          let nf c = Evarutil.nf_evar sigma c in
          let decl = Tacmach.New.pf_last_hyp (Proofview.Goal.assume gl) in
          let hyp = Context.Named.Declaration.map_constr nf decl in
	  let hintl = make_resolve_hyp env sigma hyp
	  in trivial_fail_db dbg mod_delta db_list
	       (Hint_db.add_list env sigma hintl local_db)
      end })
  in
  Proofview.Goal.enter { enter = begin fun gl ->
    let concl = Tacmach.New.pf_nf_concl gl in
    let secvars = compute_secvars gl in
    Tacticals.New.tclFIRST
      ((dbg_assumption dbg)::intro_tac::
          (List.map Tacticals.New.tclCOMPLETE
             (trivial_resolve dbg mod_delta db_list local_db secvars concl)))
  end }

and my_find_search_nodelta db_list local_db secvars hdc concl =
  List.map (fun hint -> (None,hint))
    (List.map_append (hintmap_of secvars 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 secvars hdc concl =
  let f = hintmap_of secvars 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 = auto_flags_of_state (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 ~secvars db
	      | Some hdc ->
		  if (Id.Pred.is_empty ids && Cpred.is_empty csts)
		  then Hint_db.map_auto ~secvars hdc concl db
		  else Hint_db.map_existential ~secvars hdc concl db
	    in auto_flags_of_state 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;poly=poly;db=dbname})) =
  let tactic = function
    | Res_pf (c,cl) -> unify_resolve_gen poly flags (c,cl)
    | ERes_pf _ -> Proofview.V82.tactic (fun gl -> error "eres_pf")
    | Give_exact (c, cl)  -> exact poly (c, cl)
    | Res_pf_THEN_trivial_fail (c,cl) ->
      Tacticals.New.tclTHEN
        (unify_resolve_gen poly 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 ()) (not (Option.is_empty flags)) db_list local_db)
    | Unfold_nth c ->
      Proofview.V82.tactic (fun gl ->
       if exists_evaluable_reference (pf_env gl) c then
	 tclPROGRESS (Proofview.V82.of_tactic (reduce (Unfold [AllOccurrences,c]) Locusops.onConcl)) gl
       else tclFAIL 0 (str"Unbound reference") gl)
    | Extern tacast -> 
      conclPattern concl p tacast
  in
  let pr_hint () =
    let origin = match dbname with
    | None -> mt ()
    | Some n -> str " (in " ++ str n ++ str ")"
    in
    pr_hint t ++ origin
  in
  tclLOG dbg pr_hint (run_hint t tactic)

and trivial_resolve dbg mod_delta db_list local_db secvars cl =
  try
    let head =
      try let hdconstr = decompose_app_bound cl in
	    Some 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 secvars head cl))
  with Not_found -> []

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

let trivial ?(debug=Off) lems dbnames =
  Proofview.Goal.nf_enter { enter = begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.New.project gl in
  let db_list = make_db_list dbnames in
  let d = mk_trivial_dbg debug in
  let hints = make_local_hint_db env sigma false lems in
  tclTRY_dbg d
    (trivial_fail_db d false db_list hints)
  end }

let full_trivial ?(debug=Off) lems =
  Proofview.Goal.nf_enter { enter = begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.New.project gl in
  let db_list = current_pure_db () in
  let d = mk_trivial_dbg debug in
  let hints = make_local_hint_db env sigma false lems in
  tclTRY_dbg d
    (trivial_fail_db d false db_list hints)
  end }

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 = gen_trivial ~debug lems l

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

let possible_resolve dbg mod_delta db_list local_db secvars cl =
  try
    let head =
      try let hdconstr = decompose_app_bound cl in
	    Some 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 secvars head cl)
  with Not_found -> []

let extend_local_db decl db gl =
  let env = Tacmach.New.pf_env gl in
  let sigma = Tacmach.New.project gl in
  Hint_db.add_list env sigma (make_resolve_hyp env sigma 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 =
  Tacticals.New.tclTHEN (dbg_intro dbg)
    (Proofview.Goal.enter { enter = begin fun gl ->
      let extend_local_db decl db = extend_local_db decl db gl in
      Tacticals.New.onLastDecl (fun decl -> kont (extend_local_db decl db))
    end })

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

let search d n mod_delta db_list local_db =
  let rec search d n local_db =
    (* spiwack: the test of [n] to 0 must be done independently in
       each goal. Hence the [tclEXTEND] *)
    Proofview.tclEXTEND [] begin
      if Int.equal n 0 then Tacticals.New.tclZEROMSG (str"BOUND 2") else
        Tacticals.New.tclORELSE0 (dbg_assumption d)
	  (Tacticals.New.tclORELSE0 (intro_register d (search d n) local_db)
	     ( Proofview.Goal.enter { enter = begin fun gl ->
               let concl = Tacmach.New.pf_nf_concl gl in
               let secvars = compute_secvars gl in
	       let d' = incr_dbg d in
	       Tacticals.New.tclFIRST
	         (List.map
		    (fun ntac -> Tacticals.New.tclTHEN ntac (search d' (n-1) local_db))
		    (possible_resolve d mod_delta db_list local_db secvars concl))
             end }))
    end []
  in
  search d n local_db

let default_search_depth = ref 5

let delta_auto debug mod_delta n lems dbnames =
  Proofview.Goal.nf_enter { enter = begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.New.project gl in
  let db_list = make_db_list dbnames in
  let d = mk_auto_dbg debug in
  let hints = make_local_hint_db env sigma false lems in
  tclTRY_dbg d
    (search d n mod_delta db_list hints)
  end }

let delta_auto = 
  if Flags.profile then
    let key = Profile.declare_profile "delta_auto" in
      Profile.profile5 key delta_auto
  else delta_auto

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 =
  Proofview.Goal.nf_enter { enter = begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.New.project gl in
  let db_list = current_pure_db () in
  let d = mk_auto_dbg debug in
  let hints = make_local_hint_db env sigma false lems in
  tclTRY_dbg d
    (search d n mod_delta db_list hints)
  end }

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 = full_auto !default_search_depth []

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 h_auto ?(debug=Off) n lems l = gen_auto ~debug n lems l