path: root/interp/impargs.ml

(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <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 CErrors
open Pp
open Util
open Names
open Constr
open Globnames
open Declarations
open Decl_kinds
open Lib
open Libobject
open EConstr
open Termops
open Reductionops
open Constrexpr
open Namegen

module NamedDecl = Context.Named.Declaration

(*s Flags governing the computation of implicit arguments *)

type implicits_flags = {
  auto : bool;                     (* automatic or manual only *)
  strict : bool;                   (* true = strict *)
  strongly_strict : bool;          (* true = strongly strict *)
  reversible_pattern : bool;
  contextual : bool;               (* true = contextual *)
  maximal : bool
}

let implicit_args = ref {
  auto = false;
  strict = true;
  strongly_strict = false;
  reversible_pattern = false;
  contextual = false;
  maximal = false;
}

let make_implicit_args flag =
  implicit_args := { !implicit_args with auto = flag }

let make_strict_implicit_args flag =
  implicit_args := { !implicit_args with strict = flag }

let make_strongly_strict_implicit_args flag =
  implicit_args := { !implicit_args with strongly_strict = flag }

let make_reversible_pattern_implicit_args flag =
  implicit_args := { !implicit_args with reversible_pattern = flag }

let make_contextual_implicit_args flag =
  implicit_args := { !implicit_args with contextual = flag }

let make_maximal_implicit_args flag =
  implicit_args := { !implicit_args with maximal = flag }

let is_implicit_args () = !implicit_args.auto
let is_strict_implicit_args () = !implicit_args.strict
let is_strongly_strict_implicit_args () = !implicit_args.strongly_strict
let is_reversible_pattern_implicit_args () = !implicit_args.reversible_pattern
let is_contextual_implicit_args () = !implicit_args.contextual
let is_maximal_implicit_args () = !implicit_args.maximal

let with_implicit_protection f x =
  let oflags = !implicit_args in
  try
    let rslt = f x in
    implicit_args := oflags;
    rslt
  with reraise ->
    let reraise = CErrors.push reraise in
    let () = implicit_args := oflags in
    iraise reraise

let set_maximality imps b =
  (* Force maximal insertion on ending implicits (compatibility) *)
  let is_set x = match x with None -> false | _ -> true in
  b || List.for_all is_set imps

(*s Computation of implicit arguments *)

(* We remember various information about why an argument is
   inferable as implicit

- [DepRigid] means that the implicit argument can be found by
  unification along a rigid path (we do not print the arguments of
  this kind if there is enough arguments to infer them)

- [DepFlex] means that the implicit argument can be found by unification
  along a collapsable path only (e.g. as x in (P x) where P is another
  argument) (we do (defensively) print the arguments of this kind)

- [DepFlexAndRigid] means that the least argument from which the
  implicit argument can be inferred is following a collapsable path
  but there is a greater argument from where the implicit argument is
  inferable following a rigid path (useful to know how to print a
  partial application)

- [Manual] means the argument has been explicitly set as implicit.

  We also consider arguments inferable from the conclusion but it is
  operational only if [conclusion_matters] is true.
*)

type argument_position =
  | Conclusion
  | Hyp of int

let argument_position_eq p1 p2 = match p1, p2 with
| Conclusion, Conclusion -> true
| Hyp h1, Hyp h2 -> Int.equal h1 h2
| _ -> false

let explicitation_eq ex1 ex2 = match ex1, ex2 with
| ExplByPos (i1, id1), ExplByPos (i2, id2) ->
  Int.equal i1 i2 && Option.equal Id.equal id1 id2
| ExplByName id1, ExplByName id2 ->
  Id.equal id1 id2
| _ -> false

type implicit_explanation =
  | DepRigid of argument_position
  | DepFlex of argument_position
  | DepFlexAndRigid of (*flex*) argument_position * (*rig*) argument_position
  | Manual

let argument_less = function
  | Hyp n, Hyp n' -> n<n'
  | Hyp _, Conclusion -> true
  | Conclusion, _ -> false

let update pos rig st =
  let e =
  if rig then
    match st with
      | None -> DepRigid pos
      | Some (DepRigid n as x) ->
          if argument_less (pos,n) then DepRigid pos else x
      | Some (DepFlexAndRigid (fpos,rpos) as x) ->
          if argument_less (pos,fpos) || argument_position_eq pos fpos then DepRigid pos else
          if argument_less (pos,rpos) then DepFlexAndRigid (fpos,pos) else x
      | Some (DepFlex fpos) ->
          if argument_less (pos,fpos) || argument_position_eq pos fpos then DepRigid pos
          else DepFlexAndRigid (fpos,pos)
      | Some Manual -> assert false
  else
    match st with
      | None -> DepFlex pos
      | Some (DepRigid rpos as x) ->
          if argument_less (pos,rpos) then DepFlexAndRigid (pos,rpos) else x
      | Some (DepFlexAndRigid (fpos,rpos) as x) ->
          if argument_less (pos,fpos) then DepFlexAndRigid (pos,rpos) else x
      | Some (DepFlex fpos as x) ->
          if argument_less (pos,fpos) then DepFlex pos else x
      | Some Manual -> assert false
  in Some e

(* modified is_rigid_reference with a truncated env *)
let is_flexible_reference env sigma bound depth f =
  match kind sigma f with
    | Rel n when n >= bound+depth -> (* inductive type *) false
    | Rel n when n >= depth -> (* previous argument *) true
    | Rel n -> (* since local definitions have been expanded *) false
    | Const (kn,_) ->
        let cb = Environ.lookup_constant kn env in
	(match cb.const_body with Def _ -> true | _ -> false)
    | Var id ->
        env |> Environ.lookup_named id |> NamedDecl.is_local_def
    | Ind _ | Construct _ -> false
    |  _ -> true

let push_lift d (e,n) = (push_rel d e,n+1)

let is_reversible_pattern sigma bound depth f l =
  isRel sigma f && let n = destRel sigma f in (n < bound+depth) && (n >= depth) &&
  Array.for_all (fun c -> isRel sigma c && destRel sigma c < depth) l &&
  Array.distinct l

(* Precondition: rels in env are for inductive types only *)
let add_free_rels_until strict strongly_strict revpat bound env sigma m pos acc =
  let rec frec rig (env,depth as ed) c =
    let hd = if strict then whd_all env sigma c else c in
    let c = if strongly_strict then hd else c in
    match kind sigma hd with
    | Rel n when (n < bound+depth) && (n >= depth) ->
	let i = bound + depth - n - 1 in
        acc.(i) <- update pos rig acc.(i)
    | App (f,l) when revpat && is_reversible_pattern sigma bound depth f l ->
        let i = bound + depth - EConstr.destRel sigma f - 1 in
	acc.(i) <- update pos rig acc.(i)
    | App (f,_) when rig && is_flexible_reference env sigma bound depth f ->
	if strict then () else
          iter_constr_with_full_binders sigma push_lift (frec false) ed c
    | Proj (p,c) when rig ->
      if strict then () else
        iter_constr_with_full_binders sigma push_lift (frec false) ed c
    | Case _ when rig ->
	if strict then () else
          iter_constr_with_full_binders sigma push_lift (frec false) ed c
    | Evar _ -> ()
    | _ ->
        iter_constr_with_full_binders sigma push_lift (frec rig) ed c
  in
  let () = if not (Vars.noccur_between sigma 1 bound m) then frec true (env,1) m in
  acc

(* compute the list of implicit arguments *)

let rec is_rigid_head sigma t = match kind sigma t with
  | Rel _ | Evar _ -> false
  | Ind _ | Const _ | Var _ | Sort _ -> true
  | Case (_,_,f,_) -> is_rigid_head sigma f
  | Proj (p,c) -> true
  | App (f,args) ->
      (match kind sigma f with
        | Fix ((fi,i),_) -> is_rigid_head sigma (args.(fi.(i)))
        | _ -> is_rigid_head sigma f)
  | Lambda _ | LetIn _ | Construct _ | CoFix _ | Fix _
  | Prod _ | Meta _ | Cast _ -> assert false

let is_rigid env sigma t =
  let open Context.Rel.Declaration in
  let t = whd_all env sigma t in
  match kind sigma t with
  | Prod (na,a,b) ->
     let (_,t) = splay_prod (push_rel (LocalAssum (na,a)) env) sigma b in
     is_rigid_head sigma t
  | _ -> true

let find_displayed_name_in all avoid na (env, b) =
  let envnames_b = (env, b) in
  let flag = RenamingElsewhereFor envnames_b in
  if all then compute_and_force_displayed_name_in Evd.empty flag avoid na b
  else compute_displayed_name_in Evd.empty flag avoid na b

let compute_implicits_names_gen all env sigma t =
  let open Context.Rel.Declaration in
  let rec aux env avoid names t =
    let t = whd_all env sigma t in
    match kind sigma t with
    | Prod (na,a,b) ->
       let na',avoid' = find_displayed_name_in all avoid na (names,b) in
       aux (push_rel (LocalAssum (na,a)) env) avoid' (na'::names) b
    | _ -> List.rev names
  in aux env Id.Set.empty [] t

let compute_implicits_names = compute_implicits_names_gen true

let compute_implicits_explanation_gen strict strongly_strict revpat contextual env sigma t =
  let open Context.Rel.Declaration in
  let rec aux env n t =
    let t = whd_all env sigma t in
    match kind sigma t with
    | Prod (na,a,b) ->
       add_free_rels_until strict strongly_strict revpat n env sigma a (Hyp (n+1))
         (aux (push_rel (LocalAssum (na,a)) env) (n+1) b)
    | _ ->
       let v = Array.make n None in
       if contextual then
         add_free_rels_until strict strongly_strict revpat n env sigma t Conclusion v
       else v
  in
  match kind sigma (whd_all env sigma t) with
  | Prod (na,a,b) ->
     let v = aux (push_rel (LocalAssum (na,a)) env) 1 b in
     Array.to_list v
  | _ -> []

let compute_implicits_explanation_flags env sigma f t =
  compute_implicits_explanation_gen
    (f.strict || f.strongly_strict) f.strongly_strict
    f.reversible_pattern f.contextual env sigma t

let compute_implicits_flags env sigma f all t =
  List.combine
    (compute_implicits_names_gen all env sigma t)
    (compute_implicits_explanation_flags env sigma f t)

let compute_auto_implicits env sigma flags enriching t =
  List.combine
    (compute_implicits_names env sigma t)
    (if enriching then compute_implicits_explanation_flags env sigma flags t
     else compute_implicits_explanation_gen false false false true env sigma t)

(* Extra information about implicit arguments *)

type maximal_insertion = bool (* true = maximal contextual insertion *)
type force_inference = bool (* true = always infer, never turn into evar/subgoal *)

type implicit_status =
    (* None = Not implicit *)
    (Id.t * implicit_explanation * (maximal_insertion * force_inference)) option

type implicit_side_condition = DefaultImpArgs | LessArgsThan of int

type implicits_list = implicit_side_condition * implicit_status list

let is_status_implicit = function
  | None -> false
  | _ -> true

let name_of_implicit = function
  | None -> anomaly (Pp.str "Not an implicit argument.")
  | Some (id,_,_) -> id

let maximal_insertion_of = function
  | Some (_,_,(b,_)) -> b
  | None -> anomaly (Pp.str "Not an implicit argument.")

let force_inference_of = function
  | Some (_, _, (_, b)) -> b
  | None -> anomaly (Pp.str "Not an implicit argument.")

(* [in_ctx] means we know the expected type, [n] is the index of the argument *)
let is_inferable_implicit in_ctx n = function
  | None -> false
  | Some (_,DepRigid (Hyp p),_) -> in_ctx || n >= p
  | Some (_,DepFlex (Hyp p),_) -> false
  | Some (_,DepFlexAndRigid (_,Hyp q),_) -> in_ctx || n >= q
  | Some (_,DepRigid Conclusion,_) -> in_ctx
  | Some (_,DepFlex Conclusion,_) -> false
  | Some (_,DepFlexAndRigid (_,Conclusion),_) -> in_ctx
  | Some (_,Manual,_) -> true

let positions_of_implicits (_,impls) =
  let rec aux n = function
      [] -> []
    | Some _ :: l -> n :: aux (n+1) l
    | None :: l -> aux (n+1) l
  in aux 1 impls

(* Manage user-given implicit arguments *)

let rec prepare_implicits f = function
  | [] -> []
  | (Anonymous, Some _)::_ -> anomaly (Pp.str "Unnamed implicit.")
  | (Name id, Some imp)::imps ->
      let imps' = prepare_implicits f imps in
      Some (id,imp,(set_maximality imps' f.maximal,true)) :: imps'
  | _::imps -> None :: prepare_implicits f imps

(*
If found, returns Some (x,(b,fi,fo)) and l with the entry removed,
otherwise returns None and l unchanged.
 *)
let assoc_by_pos k l =
  let rec aux = function
      (ExplByPos (k', x), b) :: tl when Int.equal k k' -> Some (x,b), tl
    | hd :: tl -> let (x, tl) = aux tl in x, hd :: tl
    | [] -> raise Not_found
  in try aux l with Not_found -> None, l

let check_correct_manual_implicits autoimps l =
  List.iter (function
    | ExplByName id,(b,fi,forced) ->
	if not forced then
	  user_err 
            (str "Wrong or non-dependent implicit argument name: " ++ Id.print id ++ str ".")
    | ExplByPos (i,_id),_t ->
	if i<1 || i>List.length autoimps then
	  user_err 
            (str "Bad implicit argument number: " ++ int i ++ str ".")
	else
	  user_err 
	    (str "Cannot set implicit argument number " ++ int i ++
	      str ": it has no name.")) l

(* Take a list l of explicitations, and map them to positions. *)
let flatten_explicitations l autoimps =
  let rec aux k l = function
    | (Name id,_)::imps ->
       let value, l' =
         try
           let eq = explicitation_eq in
           let flags = List.assoc_f eq (ExplByName id) l in
           Some (Some id, flags), List.remove_assoc_f eq (ExplByName id) l
         with Not_found -> assoc_by_pos k l
       in value :: aux (k+1) l' imps
    | (Anonymous,_)::imps ->
       let value, l' = assoc_by_pos k l
       in value :: aux (k+1) l' imps
    | [] when List.is_empty l -> []
    | [] ->
       check_correct_manual_implicits autoimps l;
       []
  in aux 1 l autoimps

let set_manual_implicits flags enriching autoimps l =
  if not (List.distinct l) then
    user_err Pp.(str "Some parameters are referred more than once.");
  (* Compare with automatic implicits to recover printing data and names *)
  let rec merge k autoimps explimps = match autoimps, explimps with
    | autoimp::autoimps, explimp::explimps ->
       let imps' = merge (k+1) autoimps explimps in
       begin match autoimp, explimp with
       | (Name id,_), Some (_, (b, fi, _)) ->
          Some (id, Manual, (set_maximality imps' b, fi))
       | (Name id,Some exp), None when enriching ->
          Some (id, exp, (set_maximality imps' flags.maximal, true))
       | (Name _,_), None -> None
       | (Anonymous,_), Some (Some id, (b, fi, true)) ->
          Some (id,Manual,(b,fi))
       | (Anonymous,_), Some (None, (b, fi, true)) ->
          let id = Id.of_string ("arg_" ^ string_of_int k) in
          Some (id,Manual,(b,fi))
       | (Anonymous,_), Some (_, (_, _, false)) -> None
       | (Anonymous,_), None -> None
       end :: imps'
    | [], [] -> []
    (* flatten_explicitations returns a list of the same length as autoimps *)
    | _ -> assert false
  in merge 1 autoimps (flatten_explicitations l autoimps)

let compute_semi_auto_implicits env sigma f t =
  if not f.auto then [DefaultImpArgs, []]
  else let l = compute_implicits_flags env sigma f false t in
       [DefaultImpArgs, prepare_implicits f l]

(*s Constants. *)

let compute_constant_implicits flags cst =
  let env = Global.env () in
  let sigma = Evd.from_env env in
  let cb = Environ.lookup_constant cst env in
  let ty = of_constr cb.const_type in
  let impls = compute_semi_auto_implicits env sigma flags ty in
  impls

(*s Inductives and constructors. Their implicit arguments are stored
   in an array, indexed by the inductive number, of pairs $(i,v)$ where
   $i$ are the implicit arguments of the inductive and $v$ the array of
   implicit arguments of the constructors. *)

let compute_mib_implicits flags kn =
  let env = Global.env () in
  let sigma = Evd.from_env env in
  let mib = Environ.lookup_mind kn env in
  let ar =
    Array.to_list
      (Array.mapi  (* No need to lift, arities contain no de Bruijn *)
        (fun i mip ->
	  (** No need to care about constraints here *)
	  let ty, _ = Global.type_of_global_in_context env (IndRef (kn,i)) in
	  Context.Rel.Declaration.LocalAssum (Name mip.mind_typename, ty))
        mib.mind_packets) in
  let env_ar = Environ.push_rel_context ar env in
  let imps_one_inductive i mip =
    let ind = (kn,i) in
    let ar, _ = Global.type_of_global_in_context env (IndRef ind) in
    ((IndRef ind,compute_semi_auto_implicits env sigma flags (of_constr ar)),
     Array.mapi (fun j c ->
       (ConstructRef (ind,j+1),compute_semi_auto_implicits env_ar sigma flags c))
       (Array.map of_constr mip.mind_nf_lc))
  in
  Array.mapi imps_one_inductive mib.mind_packets

let compute_all_mib_implicits flags kn =
  let imps = compute_mib_implicits flags kn in
  List.flatten
    (Array.map_to_list (fun (ind,cstrs) -> ind::Array.to_list cstrs) imps)

(*s Variables. *)

let compute_var_implicits flags id =
  let env = Global.env () in
  let sigma = Evd.from_env env in
  compute_semi_auto_implicits env sigma flags (NamedDecl.get_type (lookup_named id env))

(* Implicits of a global reference. *)

let compute_global_implicits flags = function
  | VarRef id -> compute_var_implicits flags id
  | ConstRef kn -> compute_constant_implicits flags kn
  | IndRef (kn,i) ->
      let ((_,imps),_) = (compute_mib_implicits flags kn).(i) in imps
  | ConstructRef ((kn,i),j) ->
      let (_,cimps) = (compute_mib_implicits flags kn).(i) in snd cimps.(j-1)

(* Merge a manual explicitation with an implicit_status list *)

let merge_impls (cond,oldimpls) (_,newimpls) =
  let oldimpls,usersuffiximpls = List.chop (List.length newimpls) oldimpls in
  cond, (List.map2 (fun orig ni ->
    match orig with
    | Some (_, Manual, _) -> orig
    | _ -> ni) oldimpls newimpls)@usersuffiximpls

(* Caching implicits *)

type implicit_interactive_request =
  | ImplAuto
  | ImplManual of int

type implicit_discharge_request =
  | ImplLocal
  | ImplConstant of Constant.t * implicits_flags
  | ImplMutualInductive of MutInd.t * implicits_flags
  | ImplInteractive of GlobRef.t * implicits_flags *
      implicit_interactive_request

let implicits_table = Summary.ref Refmap.empty ~name:"implicits"

let implicits_of_global ref =
  try
    let l = Refmap.find ref !implicits_table in
    try
      let rename_l = Arguments_renaming.arguments_names ref in
      let rec rename implicits names = match implicits, names with
        | [], _ -> []
        | _, [] -> implicits
        | Some (_, x,y) :: implicits, Name id :: names ->
           Some (id, x,y) :: rename implicits names
        | imp :: implicits, _ :: names -> imp :: rename implicits names
      in
      List.map (fun (t, il) -> t, rename il rename_l) l
    with Not_found -> l
  with Not_found -> [DefaultImpArgs,[]]

let cache_implicits_decl (ref,imps) =
  implicits_table := Refmap.add ref imps !implicits_table

let load_implicits _ (_,(_,l)) = List.iter cache_implicits_decl l

let cache_implicits o =
  load_implicits 1 o

let subst_implicits_decl subst (r,imps as o) =
  let r' = fst (subst_global subst r) in if r==r' then o else (r',imps)

let subst_implicits (subst,(req,l)) =
  (ImplLocal,List.Smart.map (subst_implicits_decl subst) l)

let impls_of_context ctx =
  let map (decl, impl) = match impl with
  | Implicit -> Some (NamedDecl.get_id decl, Manual, (true, true))
  | _ -> None
  in
  List.rev_map map (List.filter (fst %> NamedDecl.is_local_assum) ctx)

let adjust_side_condition p = function
  | LessArgsThan n -> LessArgsThan (n+p)
  | DefaultImpArgs -> DefaultImpArgs

let add_section_impls vars extra_impls (cond,impls) =
  let p = List.length vars - List.length extra_impls in
  adjust_side_condition p cond, extra_impls @ impls

let discharge_implicits (_,(req,l)) =
  match req with
  | ImplLocal -> None
  | ImplInteractive (ref,flags,exp) ->
    (try
      let vars = variable_section_segment_of_reference ref in
      let ref' = if isVarRef ref then ref else pop_global_reference ref in
      let extra_impls = impls_of_context vars in
      let l' = [ref', List.map (add_section_impls vars extra_impls) (snd (List.hd l))] in
      Some (ImplInteractive (ref',flags,exp),l')
    with Not_found -> (* ref not defined in this section *) Some (req,l))
  | ImplConstant (con,flags) ->
    (try
      let con' = pop_con con in
      let vars = variable_section_segment_of_reference (ConstRef con) in
      let extra_impls = impls_of_context vars in
      let newimpls = List.map (add_section_impls vars extra_impls) (snd (List.hd l)) in
      let l' = [ConstRef con',newimpls] in
	Some (ImplConstant (con',flags),l')
    with Not_found -> (* con not defined in this section *) Some (req,l))
  | ImplMutualInductive (kn,flags) ->
    (try
      let l' = List.map (fun (gr, l) ->
	let vars = variable_section_segment_of_reference gr in
	let extra_impls = impls_of_context vars in
	((if isVarRef gr then gr else pop_global_reference gr),
	 List.map (add_section_impls vars extra_impls) l)) l
      in
	Some (ImplMutualInductive (pop_kn kn,flags),l')
    with Not_found -> (* ref not defined in this section *) Some (req,l))

let rebuild_implicits (req,l) =
  match req with
  | ImplLocal -> assert false
  | ImplConstant (con,flags) ->
      let oldimpls = snd (List.hd l) in
      let newimpls = compute_constant_implicits flags con in
      req, [ConstRef con, List.map2 merge_impls oldimpls newimpls]
  | ImplMutualInductive (kn,flags) ->
      let newimpls = compute_all_mib_implicits flags kn in
      let rec aux olds news =
       match olds, news with
       | (_, oldimpls) :: old, (gr, newimpls) :: tl ->
          (gr, List.map2 merge_impls oldimpls newimpls) :: aux old tl
       | [], [] -> []
       | _, _ -> assert false
      in req, aux l newimpls

  | ImplInteractive (ref,flags,o) ->
      (if isVarRef ref && is_in_section ref then ImplLocal else req),
      match o with
      | ImplAuto ->
         let oldimpls = snd (List.hd l) in
         let newimpls = compute_global_implicits flags ref in
         [ref,List.map2 merge_impls oldimpls newimpls]
      | ImplManual userimplsize ->
         let oldimpls = snd (List.hd l) in
         if flags.auto then
           let newimpls = List.hd (compute_global_implicits flags ref) in
           let p = List.length (snd newimpls) - userimplsize in
           let newimpls = on_snd (List.firstn p) newimpls in
           [ref,List.map (fun o -> merge_impls o newimpls) oldimpls]
         else
           [ref,oldimpls]

let classify_implicits (req,_ as obj) = match req with
| ImplLocal -> Dispose
| _ -> Substitute obj

type implicits_obj =
    implicit_discharge_request *
      (GlobRef.t * implicits_list list) list

let inImplicits : implicits_obj -> obj =
  declare_object {(default_object "IMPLICITS") with
    cache_function = cache_implicits;
    load_function = load_implicits;
    subst_function = subst_implicits;
    classify_function = classify_implicits;
    discharge_function = discharge_implicits;
    rebuild_function = rebuild_implicits }

let is_local local ref = local || isVarRef ref && is_in_section ref

let declare_implicits_gen req flags ref =
  let imps = compute_global_implicits flags ref in
  add_anonymous_leaf (inImplicits (req,[ref,imps]))

let declare_implicits local ref =
  let flags = { !implicit_args with auto = true } in
  let req =
    if is_local local ref then ImplLocal else ImplInteractive(ref,flags,ImplAuto) in
    declare_implicits_gen req flags ref

let declare_var_implicits id =
  let flags = !implicit_args in
    declare_implicits_gen ImplLocal flags (VarRef id)

let declare_constant_implicits con =
  let flags = !implicit_args in
    declare_implicits_gen (ImplConstant (con,flags)) flags (ConstRef con)

let declare_mib_implicits kn =
  let flags = !implicit_args in
  let imps = Array.map_to_list
    (fun (ind,cstrs) -> ind::(Array.to_list cstrs))
    (compute_mib_implicits flags kn) in
    add_anonymous_leaf
      (inImplicits (ImplMutualInductive (kn,flags),List.flatten imps))

(* Declare manual implicits *)
type manual_explicitation = Constrexpr.explicitation * (bool * bool * bool)

type manual_implicits = manual_explicitation list

let compute_implicits_with_manual env sigma typ enriching l =
  let autoimpls = compute_auto_implicits env sigma !implicit_args enriching typ in
  set_manual_implicits !implicit_args enriching autoimpls l

let check_inclusion l =
  (* Check strict inclusion *)
  let rec aux = function
    | n1::(n2::_ as nl) ->
	if n1 <= n2 then
	  user_err Pp.(str "Sequences of implicit arguments must be of different lengths.");
	aux nl
    | _ -> () in
  aux (List.map (fun (imps,_) -> List.length imps) l)

let check_rigidity isrigid =
  if not isrigid then
    user_err  (strbrk "Multiple sequences of implicit arguments available only for references that cannot be applied to an arbitrarily large number of arguments.")

let projection_implicits env p impls = 
  let pb = Environ.lookup_projection p env in
    CList.skipn_at_least pb.Declarations.proj_npars impls

let declare_manual_implicits local ref ?enriching l =
  let flags = !implicit_args in
  let env = Global.env () in
  let sigma = Evd.from_env env in
  let t, _ = Global.type_of_global_in_context env ref in
  let t = of_constr t in
  let enriching = Option.default flags.auto enriching in
  let autoimpls = compute_auto_implicits env sigma flags enriching t in
  let l' = match l with
    | [] -> assert false
    | [l] ->
       [DefaultImpArgs, set_manual_implicits flags enriching autoimpls l]
    | _ ->
       check_rigidity (is_rigid env sigma t);
       let l = List.map (fun imps -> (imps,List.length imps)) l in
       let l = List.sort (fun (_,n1) (_,n2) -> n2 - n1) l in
       check_inclusion l;
       let nargs = List.length autoimpls in
       List.map (fun (imps,n) ->
           (LessArgsThan (nargs-n),
            set_manual_implicits flags enriching autoimpls imps)) l in
  let req =
    if is_local local ref then ImplLocal
    else ImplInteractive(ref,flags,ImplManual (List.length autoimpls))
  in add_anonymous_leaf (inImplicits (req,[ref,l']))

let maybe_declare_manual_implicits local ref ?enriching l =
  match l with
  | [] -> ()
  | _ -> declare_manual_implicits local ref ?enriching [l]

let extract_impargs_data impls =
  let rec aux p = function
    | (DefaultImpArgs, imps)::_ -> [None,imps]
    | (LessArgsThan n, imps)::l -> (Some (p,n),imps) :: aux (n+1) l
    | [] -> [] in
  aux 0 impls

let lift_implicits n =
  List.map (fun x ->
    match fst x with
	ExplByPos (k, id) -> ExplByPos (k + n, id), snd x
      | _ -> x)

let make_implicits_list l = [DefaultImpArgs, l]

let rec drop_first_implicits p l =
  if Int.equal p 0 then l else match l with
  | _,[] as x -> x
  | DefaultImpArgs,imp::impls ->
      drop_first_implicits (p-1) (DefaultImpArgs,impls)
  | LessArgsThan n,imp::impls ->
      let n = if is_status_implicit imp then n-1 else n in
      drop_first_implicits (p-1) (LessArgsThan n,impls)

let rec select_impargs_size n = function
  | [] -> [] (* Tolerance for (DefaultImpArgs,[]) *)
  | [_, impls] | (DefaultImpArgs, impls)::_ -> impls
  | (LessArgsThan p, impls)::l ->
      if n <= p then impls else select_impargs_size n l

let select_stronger_impargs = function
  | [] -> [] (* Tolerance for (DefaultImpArgs,[]) *)
  | (_,impls)::_ -> impls