path: root/interp/impargs.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open CErrors
open Util
open Names
open Globnames
open Nameops
open Term
open Reduction
open Declarations
open Environ
open Libobject
open Lib
open Pp
open Constrexpr
open Termops
open Namegen
open Decl_kinds
open Context.Named.Declaration

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 (na,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 na, Some e

(* modified is_rigid_reference with a truncated env *)
let is_flexible_reference env bound depth f =
  match kind_of_term 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 |> is_local_def
    | Ind _ | Construct _ -> false
    |  _ -> true

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

let is_reversible_pattern bound depth f l =
  isRel f && let n = destRel f in (n < bound+depth) && (n >= depth) &&
  Array.for_all (fun c -> isRel c && destRel 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 m pos acc =
  let rec frec rig (env,depth as ed) c =
    let hd = if strict then whd_all env c else c in
    let c = if strongly_strict then hd else c in
    match kind_of_term 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 bound depth f l ->
	let i = bound + depth - destRel f - 1 in
	acc.(i) <- update pos rig acc.(i)
    | App (f,_) when rig && is_flexible_reference env bound depth f ->
	if strict then () else
          iter_constr_with_full_binders push_lift (frec false) ed c
    | Proj (p,c) when rig ->
      if strict then () else
        iter_constr_with_full_binders push_lift (frec false) ed c	  
    | Case _ when rig ->
	if strict then () else
          iter_constr_with_full_binders push_lift (frec false) ed c
    | Evar _ -> ()
    | _ ->
        iter_constr_with_full_binders push_lift (frec rig) ed c
  in
  let () = if not (Vars.noccur_between 1 bound m) then frec true (env,1) m in
  acc

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

(* calcule la liste des arguments implicites *)

let find_displayed_name_in all avoid na (env, b) =
  let b = EConstr.of_constr b in
  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_gen strict strongly_strict revpat contextual all env t =
  let rigid = ref true in
  let open Context.Rel.Declaration in
  let rec aux env avoid n names t =
    let t = whd_all env t in
    match kind_of_term t with
      | Prod (na,a,b) ->
	  let na',avoid' = find_displayed_name_in all avoid na (names,b) in
	  add_free_rels_until strict strongly_strict revpat n env a (Hyp (n+1))
            (aux (push_rel (LocalAssum (na',a)) env) avoid' (n+1) (na'::names) b)
      | _ ->
	  rigid := is_rigid_head t;
	  let names = List.rev names in
	  let v = Array.map (fun na -> na,None) (Array.of_list names) in
	  if contextual then
	    add_free_rels_until strict strongly_strict revpat n env t Conclusion v
	  else v
  in
  match kind_of_term (whd_all env t) with
    | Prod (na,a,b) ->
	let na',avoid = find_displayed_name_in all Id.Set.empty na ([],b) in
	let v = aux (push_rel (LocalAssum (na',a)) env) avoid 1 [na'] b in
	!rigid, Array.to_list v
    | _ -> true, []

let compute_implicits_flags env f all t =
  compute_implicits_gen
    (f.strict || f.strongly_strict) f.strongly_strict
    f.reversible_pattern f.contextual all env t

let compute_auto_implicits env flags enriching t =
  if enriching then compute_implicits_flags env flags true t
  else compute_implicits_gen false false false true true env t

let compute_implicits_names env t =
  let _, impls = compute_implicits_gen false false false false true env t in
  List.map fst impls

(* 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

let set_implicit id imp insmax =
  (id,(match imp with None -> Manual | Some imp -> imp),insmax)

let rec assoc_by_pos k = function
    (ExplByPos (k', x), b) :: tl when Int.equal k k' -> (x,b), tl
  | hd :: tl -> let (x, tl) = assoc_by_pos k tl in x, hd :: tl
  | [] -> raise Not_found

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: " ++ pr_id 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

let set_manual_implicits env flags enriching autoimps l =
  let try_forced k l =
    try
      let (id, (b, fi, fo)), l' = assoc_by_pos k l in
	if fo then
	  let id = match id with Some id -> id | None -> Id.of_string ("arg_" ^ string_of_int k) in
	    l', Some (id,Manual,(b,fi))
	else l, None
    with Not_found -> l, None
  in
  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 l = function
  | (Name id,imp)::imps ->
      let l',imp,m =
	try
          let eq = explicitation_eq in
	  let (b, fi, fo) = List.assoc_f eq (ExplByName id) l in
	  List.remove_assoc_f eq (ExplByName id) l, (Some Manual), (Some (b, fi))
	with Not_found ->
	try
	  let (id, (b, fi, fo)), l' = assoc_by_pos k l in
	    l', (Some Manual), (Some (b,fi))
	with Not_found ->
          let m = match enriching, imp with
          | true, Some _ -> Some (flags.maximal, true)
          | _ -> None
          in
          l, imp, m
      in
      let imps' = merge (k+1) l' imps in
      let m = Option.map (fun (b,f) -> 
	(* match imp with Some Manual -> (b,f) *)
	(* | _ ->  *)set_maximality imps' b, f) m in
      Option.map (set_implicit id imp) m :: imps'
  | (Anonymous,imp)::imps ->
      let l', forced = try_forced k l in
	forced :: merge (k+1) l' imps
  | [] when begin match l with [] -> true | _ -> false end -> []
  | [] ->
      check_correct_manual_implicits autoimps l;
      []
  in
  merge 1 l autoimps

let compute_semi_auto_implicits env f manual t =
  match manual with
  | [] ->
      if not f.auto then [DefaultImpArgs, []]
      else let _,l = compute_implicits_flags env f false t in
	     [DefaultImpArgs, prepare_implicits f l]
  | _ ->
      let _,autoimpls = compute_auto_implicits env f f.auto t in
      [DefaultImpArgs, set_manual_implicits env f f.auto autoimpls manual]

(*s Constants. *)

let compute_constant_implicits flags manual cst =
  let env = Global.env () in
  let cb = Environ.lookup_constant cst env in
  let ty = cb.const_type in
  let impls = compute_semi_auto_implicits env flags manual 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 manual kn =
  let env = Global.env () in
  let mib = 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 = 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 flags manual ar),
     Array.mapi (fun j c ->
       (ConstructRef (ind,j+1),compute_semi_auto_implicits env_ar flags manual c))
       mip.mind_nf_lc)
  in
  Array.mapi imps_one_inductive mib.mind_packets

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

(*s Variables. *)

let compute_var_implicits flags manual id =
  let env = Global.env () in
  compute_semi_auto_implicits env flags manual (NamedDecl.get_type (lookup_named id env))

(* Implicits of a global reference. *)

let compute_global_implicits flags manual = function
  | VarRef id -> compute_var_implicits flags manual id
  | ConstRef kn -> compute_constant_implicits flags manual kn
  | IndRef (kn,i) ->
      let ((_,imps),_) = (compute_mib_implicits flags manual kn).(i) in imps
  | ConstructRef ((kn,i),j) ->
      let (_,cimps) = (compute_mib_implicits flags manual 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 * implicits_flags
  | ImplMutualInductive of mutual_inductive * implicits_flags
  | ImplInteractive of global_reference * 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.smartmap (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 %> 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,_,_ = section_segment_of_constant 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 *
      (global_reference * 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 typ enriching l =
  let _,autoimpls = compute_auto_implicits env !implicit_args enriching typ in
  set_manual_implicits env !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 t, _ = Global.type_of_global_in_context (Global.env ()) ref in
  let enriching = Option.default flags.auto enriching in
  let isrigid,autoimpls = compute_auto_implicits env flags enriching t in
  let l' = match l with
    | [] -> assert false
    | [l] ->
	[DefaultImpArgs, set_manual_implicits env flags enriching autoimpls l]
    | _ ->
	check_rigidity isrigid;
	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 env 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