(************************************************************************)
(*  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 Errors
open Util
open Names
open Nameops
open Term
open Vars
open Termops
open Environ
open Globnames

(** Generic filters *)
module Filter :
sig
  type t
  val equal : t -> t -> bool
  val identity : t
  val filter_list : t -> 'a list -> 'a list
  val filter_array : t -> 'a array -> 'a array
  val extend : int -> t -> t
  val compose : t -> t -> t
  val apply_subfilter : t -> bool list -> t
  val restrict_upon : t -> int -> (int -> bool) -> t option
  val map_along : (bool -> 'a -> bool) -> t -> 'a list -> t
  val make : bool list -> t
  val repr :  t -> bool list option
end =
struct
  type t = bool list option
  (** We guarantee through the interface that if a filter is [Some _] then it
      contains at least one [false] somewhere. *)

  let identity = None

  let rec equal l1 l2 = match l1, l2 with
  | [], [] -> true
  | h1 :: l1, h2 :: l2 ->
    (if h1 then h2 else not h2) && equal l1 l2
  | _ -> false

  let equal l1 l2 = match l1, l2 with
  | None, None -> true
  | Some _, None | None, Some _ -> false
  | Some l1, Some l2 -> equal l1 l2

  let rec is_identity = function
  | [] -> true
  | true :: l -> is_identity l
  | false :: _ -> false

  let normalize f = if is_identity f then None else Some f

  let filter_list f l = match f with
  | None -> l
  | Some f -> CList.filter_with f l

  let filter_array f v = match f with
  | None -> v
  | Some f -> CArray.filter_with f v

  let rec extend n l =
    if n = 0 then l
    else extend (pred n) (true :: l)

  let extend n = function
  | None -> None
  | Some f -> Some (extend n f)

  let compose f1 f2 = match f1 with
  | None -> f2
  | Some f1 ->
    match f2 with
    | None -> None
    | Some f2 -> normalize (CList.filter_with f1 f2)

  let apply_subfilter_array filter subfilter =
    (** In both cases we statically know that the argument will contain at
        least one [false] *)
    match filter with
    | None -> Some (Array.to_list subfilter)
    | Some f ->
    let len = Array.length subfilter in
    let fold b (i, ans) =
      if b then
        let () = assert (0 <= i) in
        (pred i, Array.unsafe_get subfilter i :: ans)
      else
        (i, false :: ans)
    in
    Some (snd (List.fold_right fold f (pred len, [])))

  let apply_subfilter filter subfilter =
    apply_subfilter_array filter (Array.of_list subfilter)

  let restrict_upon f len p =
    let newfilter = Array.init len p in
    if Array.for_all (fun id -> id) newfilter then None
    else
      Some (apply_subfilter_array f newfilter)

  let map_along f flt l =
    let ans = match flt with
    | None -> List.map (fun x -> f true x) l
    | Some flt -> List.map2 f flt l
    in
    normalize ans

  let make l = normalize l

  let repr f = f

end

(* The kinds of existential variables are now defined in [Evar_kinds] *)

(* The type of mappings for existential variables *)

module Dummy = struct end
module Store = Store.Make(Dummy)

type evar = Term.existential_key

let string_of_existential evk = "?X" ^ string_of_int (Evar.repr evk)

type evar_body =
  | Evar_empty
  | Evar_defined of constr

type evar_info = {
  evar_concl : constr;
  evar_hyps : named_context_val;
  evar_body : evar_body;
  evar_filter : Filter.t;
  evar_source : Evar_kinds.t Loc.located;
  evar_candidates : constr list option; (* if not None, list of allowed instances *)
  evar_extra : Store.t }

let make_evar hyps ccl = {
  evar_concl = ccl;
  evar_hyps = hyps;
  evar_body = Evar_empty;
  evar_filter = Filter.identity;
  evar_source = (Loc.ghost,Evar_kinds.InternalHole);
  evar_candidates = None;
  evar_extra = Store.empty
}

let instance_mismatch () =
  anomaly (Pp.str "Signature and its instance do not match")

let evar_concl evi = evi.evar_concl

let evar_filter evi = evi.evar_filter

let evar_body evi = evi.evar_body

let evar_context evi = named_context_of_val evi.evar_hyps

let evar_filtered_context evi =
  Filter.filter_list (evar_filter evi) (evar_context evi)

let evar_hyps evi = evi.evar_hyps

let evar_filtered_hyps evi = match Filter.repr (evar_filter evi) with
| None -> evar_hyps evi
| Some filter ->
  let rec make_hyps filter ctxt = match filter, ctxt with
  | [], [] -> empty_named_context_val
  | false :: filter, _ :: ctxt -> make_hyps filter ctxt
  | true :: filter, decl :: ctxt ->
    let hyps = make_hyps filter ctxt in
    push_named_context_val decl hyps
  | _ -> instance_mismatch ()
  in
  make_hyps filter (evar_context evi)

let evar_env evi = Global.env_of_context evi.evar_hyps

let evar_filtered_env evi = match Filter.repr (evar_filter evi) with
| None -> evar_env evi
| Some filter ->
  let rec make_env filter ctxt = match filter, ctxt with
  | [], [] -> reset_context (Global.env ())
  | false :: filter, _ :: ctxt -> make_env filter ctxt
  | true :: filter, decl :: ctxt ->
    let env = make_env filter ctxt in
    push_named decl env
  | _ -> instance_mismatch ()
  in
  make_env filter (evar_context evi)

let map_evar_body f = function
  | Evar_empty -> Evar_empty
  | Evar_defined d -> Evar_defined (f d)

let map_evar_info f evi =
  {evi with
    evar_body = map_evar_body f evi.evar_body;
    evar_hyps = map_named_val f evi.evar_hyps;
    evar_concl = f evi.evar_concl;
    evar_candidates = Option.map (List.map f) evi.evar_candidates }

(* This exception is raised by *.existential_value *)
exception NotInstantiatedEvar

(* Note: let-in contributes to the instance *)

let evar_instance_array test_id info args =
  let len = Array.length args in
  let rec instrec filter ctxt i = match filter, ctxt with
  | [], [] ->
    if Int.equal i len then []
    else instance_mismatch ()
  | false :: filter, _ :: ctxt ->
    instrec filter ctxt i
  | true :: filter, (id,_,_ as d) :: ctxt ->
    if i < len then
      let c = Array.unsafe_get args i in
      if test_id d c then instrec filter ctxt (succ i)
      else (id, c) :: instrec filter ctxt (succ i)
    else instance_mismatch ()
  | _ -> instance_mismatch ()
  in
  match Filter.repr (evar_filter info) with
  | None ->
    let map i (id,_,_ as d) =
      if (i < len) then
        let c = Array.unsafe_get args i in
        if test_id d c then None else Some (id,c)
      else instance_mismatch ()
    in
    List.map_filter_i map (evar_context info)
  | Some filter ->
    instrec filter (evar_context info) 0

let make_evar_instance_array info args =
  evar_instance_array (fun (id,_,_) -> isVarId id) info args

let instantiate_evar_array info c args =
  let inst = make_evar_instance_array info args in
  match inst with
  | [] -> c
  | _ -> replace_vars inst c

module StringOrd = struct type t = string let compare = String.compare end
module UNameMap = struct
    
  include Map.Make(StringOrd)
    
  let union s t = 
    if s == t then s
    else
      merge (fun k l r -> 
	match l, r with
	| Some _, _ -> l
	| _, _ -> r) s t
end

(* 2nd part used to check consistency on the fly. *)
type evar_universe_context = 
 { uctx_names : Univ.Level.t UNameMap.t * string Univ.LMap.t;
   uctx_local : Univ.universe_context_set; (** The local context of variables *)
   uctx_univ_variables : Universes.universe_opt_subst;
   (** The local universes that are unification variables *)
   uctx_univ_algebraic : Univ.universe_set; 
   (** The subset of unification variables that can be instantiated with
	algebraic universes as they appear in inferred types only. *)
   uctx_universes : Univ.universes; (** The current graph extended with the local constraints *)
   uctx_initial_universes : Univ.universes; (** The graph at the creation of the evar_map *)
 }
  
let empty_evar_universe_context = 
  { uctx_names = UNameMap.empty, Univ.LMap.empty;
    uctx_local = Univ.ContextSet.empty;
    uctx_univ_variables = Univ.LMap.empty;
    uctx_univ_algebraic = Univ.LSet.empty;
    uctx_universes = Univ.initial_universes;
    uctx_initial_universes = Univ.initial_universes }

let evar_universe_context_from e = 
  let u = universes e in
    {empty_evar_universe_context with 
      uctx_universes = u; uctx_initial_universes = u}

let is_empty_evar_universe_context ctx =
  Univ.ContextSet.is_empty ctx.uctx_local && 
    Univ.LMap.is_empty ctx.uctx_univ_variables

let union_evar_universe_context ctx ctx' =
  if ctx == ctx' then ctx
  else if is_empty_evar_universe_context ctx' then ctx
  else
    let local = Univ.ContextSet.union ctx.uctx_local ctx'.uctx_local in
    let names = UNameMap.union (fst ctx.uctx_names) (fst ctx'.uctx_names) in
    let newus = Univ.LSet.diff (Univ.ContextSet.levels ctx'.uctx_local)
			       (Univ.ContextSet.levels ctx.uctx_local) in
    let newus = Univ.LSet.diff newus (Univ.LMap.domain ctx.uctx_univ_variables) in
    let declarenew g =
      Univ.LSet.fold (fun u g -> Univ.add_universe u false g) newus g
    in
    let names_rev = Univ.LMap.union (snd ctx.uctx_names) (snd ctx'.uctx_names) in
      { uctx_names = (names, names_rev);
	uctx_local = local;
	uctx_univ_variables = 
	  Univ.LMap.subst_union ctx.uctx_univ_variables ctx'.uctx_univ_variables;
	uctx_univ_algebraic = 
	  Univ.LSet.union ctx.uctx_univ_algebraic ctx'.uctx_univ_algebraic;
	uctx_initial_universes = declarenew ctx.uctx_initial_universes;
	uctx_universes = 
	  if local == ctx.uctx_local then ctx.uctx_universes
	  else
	    let cstrsr = Univ.ContextSet.constraints ctx'.uctx_local in
	      Univ.merge_constraints cstrsr (declarenew ctx.uctx_universes) }

(* let union_evar_universe_context_key = Profile.declare_profile "union_evar_universe_context";; *)
(* let union_evar_universe_context =  *)
(*   Profile.profile2 union_evar_universe_context_key union_evar_universe_context;; *)

type 'a in_evar_universe_context = 'a * evar_universe_context

let evar_universe_context_set diff ctx =
  let initctx = ctx.uctx_local in
  let cstrs =
    Univ.LSet.fold
      (fun l cstrs ->
       try
	 match Univ.LMap.find l ctx.uctx_univ_variables with
	 | Some u -> Univ.Constraint.add (l, Univ.Eq, Option.get (Univ.Universe.level u)) cstrs
	 | None -> cstrs
       with Not_found | Option.IsNone -> cstrs)
      (Univ.Instance.levels (Univ.UContext.instance diff)) Univ.Constraint.empty
  in
    Univ.ContextSet.add_constraints cstrs initctx 
		      
let evar_universe_context_constraints ctx = snd ctx.uctx_local
let evar_context_universe_context ctx = Univ.ContextSet.to_context ctx.uctx_local
    
let evar_universe_context_of ctx = { empty_evar_universe_context with uctx_local = ctx }
let evar_universe_context_subst ctx = ctx.uctx_univ_variables

let add_uctx_names s l (names, names_rev) =
  (UNameMap.add s l names, Univ.LMap.add l s names_rev)

let evar_universe_context_of_binders b =
  let ctx = empty_evar_universe_context in
  let names =
    List.fold_left (fun acc (id, l) -> add_uctx_names (Id.to_string id) l acc)
		   ctx.uctx_names b
  in { ctx with uctx_names = names }
					
let instantiate_variable l b v =
  v := Univ.LMap.add l (Some b) !v

exception UniversesDiffer

let process_universe_constraints univs vars alg cstrs =
  let vars = ref vars in
  let normalize = Universes.normalize_universe_opt_subst vars in
  let rec unify_universes fo l d r local =
    let l = normalize l and r = normalize r in
      if Univ.Universe.equal l r then local
      else 
	let varinfo x = 
	  match Univ.Universe.level x with
	  | None -> Inl x
	  | Some l -> Inr (l, Univ.LMap.mem l !vars, Univ.LSet.mem l alg)
	in
	  if d == Universes.ULe then
	    if Univ.check_leq univs l r then
	      (** Keep Prop/Set <= var around if var might be instantiated by prop or set
		  later. *)
	      if Univ.Universe.is_level l then 
		match Univ.Universe.level r with
		| Some r ->
		  Univ.Constraint.add (Option.get (Univ.Universe.level l),Univ.Le,r) local
		| _ -> local
	      else local
	    else
	      match Univ.Universe.level r with
	      | None -> error ("Algebraic universe on the right")
	      | Some rl ->
		if Univ.Level.is_small rl then
		  let levels = Univ.Universe.levels l in
		    Univ.LSet.fold (fun l local ->
		      if Univ.Level.is_small l || Univ.LMap.mem l !vars then
			unify_universes fo (Univ.Universe.make l) Universes.UEq r local
		      else raise (Univ.UniverseInconsistency (Univ.Le, Univ.Universe.make l, r, None)))
		      levels local
		else
		  Univ.enforce_leq l r local
	  else if d == Universes.ULub then
	    match varinfo l, varinfo r with
	    | (Inr (l, true, _), Inr (r, _, _)) 
	    | (Inr (r, _, _), Inr (l, true, _)) -> 
	      instantiate_variable l (Univ.Universe.make r) vars; 
	      Univ.enforce_eq_level l r local
	    | Inr (_, _, _), Inr (_, _, _) ->
	      unify_universes true l Universes.UEq r local
	    | _, _ -> assert false
	  else (* d = Universes.UEq *)
	    match varinfo l, varinfo r with
	    | Inr (l', lloc, _), Inr (r', rloc, _) ->
	      let () = 
		if lloc then
		  instantiate_variable l' r vars
		else if rloc then 
		  instantiate_variable r' l vars
		else if not (Univ.check_eq univs l r) then
		  (* Two rigid/global levels, none of them being local,
		     one of them being Prop/Set, disallow *)
		  if Univ.Level.is_small l' || Univ.Level.is_small r' then
		    raise (Univ.UniverseInconsistency (Univ.Eq, l, r, None))
		  else
		    if fo then 
		      raise UniversesDiffer
	      in
	        Univ.enforce_eq_level l' r' local
	    | Inr (l, loc, alg), Inl r
	    | Inl r, Inr (l, loc, alg) ->
	       let inst = Univ.univ_level_rem l r r in
		 if alg then (instantiate_variable l inst vars; local)
		 else
		   let lu = Univ.Universe.make l in
		   if Univ.univ_level_mem l r then
		     Univ.enforce_leq inst lu local
		   else raise (Univ.UniverseInconsistency (Univ.Eq, lu, r, None))
            | _, _ (* One of the two is algebraic or global *) -> 
	     if Univ.check_eq univs l r then local
	     else raise (Univ.UniverseInconsistency (Univ.Eq, l, r, None))
  in
  let local = 
    Universes.Constraints.fold (fun (l,d,r) local -> unify_universes false l d r local)
      cstrs Univ.Constraint.empty
  in
    !vars, local

let add_constraints_context ctx cstrs =
  let univs, local = ctx.uctx_local in
  let cstrs' = Univ.Constraint.fold (fun (l,d,r) acc -> 
    let l = Univ.Universe.make l and r = Univ.Universe.make r in
    let cstr' = 
      if d == Univ.Lt then (Univ.Universe.super l, Universes.ULe, r)
      else (l, (if d == Univ.Le then Universes.ULe else Universes.UEq), r)
    in Universes.Constraints.add cstr' acc)
    cstrs Universes.Constraints.empty
  in
  let vars, local' =
    process_universe_constraints ctx.uctx_universes
      ctx.uctx_univ_variables ctx.uctx_univ_algebraic
      cstrs'
  in
    { ctx with uctx_local = (univs, Univ.Constraint.union local local');
      uctx_univ_variables = vars;
      uctx_universes = Univ.merge_constraints local' ctx.uctx_universes }

(* let addconstrkey = Profile.declare_profile "add_constraints_context";; *)
(* let add_constraints_context = Profile.profile2 addconstrkey add_constraints_context;; *)

let add_universe_constraints_context ctx cstrs =
  let univs, local = ctx.uctx_local in
  let vars, local' = 
    process_universe_constraints ctx.uctx_universes 
      ctx.uctx_univ_variables ctx.uctx_univ_algebraic 
      cstrs 
  in
    { ctx with uctx_local = (univs, Univ.Constraint.union local local');
      uctx_univ_variables = vars;
      uctx_universes = Univ.merge_constraints local' ctx.uctx_universes }

(* let addunivconstrkey = Profile.declare_profile "add_universe_constraints_context";; *)
(* let add_universe_constraints_context =  *)
(*   Profile.profile2 addunivconstrkey add_universe_constraints_context;; *)
(*******************************************************************)
(* Metamaps *)

(*******************************************************************)
(*            Constraints for existential variables                *)
(*******************************************************************)

type 'a freelisted = {
  rebus : 'a;
  freemetas : Int.Set.t }

(* Collects all metavars appearing in a constr *)
let metavars_of c =
  let rec collrec acc c =
    match kind_of_term c with
      | Meta mv -> Int.Set.add mv acc
      | _         -> fold_constr collrec acc c
  in
  collrec Int.Set.empty c

let mk_freelisted c =
  { rebus = c; freemetas = metavars_of c }

let map_fl f cfl = { cfl with rebus=f cfl.rebus }

(* Status of an instance found by unification wrt to the meta it solves:
  - a supertype of the meta (e.g. the solution to ?X <= T is a supertype of ?X)
  - a subtype of the meta (e.g. the solution to T <= ?X is a supertype of ?X)
  - a term that can be eta-expanded n times while still being a solution
    (e.g. the solution [P] to [?X u v = P u v] can be eta-expanded twice)
*)

type instance_constraint = IsSuperType | IsSubType | Conv

let eq_instance_constraint c1 c2 = c1 == c2

(* Status of the unification of the type of an instance against the type of
     the meta it instantiates:
   - CoerceToType means that the unification of types has not been done
     and that a coercion can still be inserted: the meta should not be
     substituted freely (this happens for instance given via the
     "with" binding clause).
   - TypeProcessed means that the information obtainable from the
     unification of types has been extracted.
   - TypeNotProcessed means that the unification of types has not been
     done but it is known that no coercion may be inserted: the meta
     can be substituted freely.
*)

type instance_typing_status =
    CoerceToType | TypeNotProcessed | TypeProcessed

(* Status of an instance together with the status of its type unification *)

type instance_status = instance_constraint * instance_typing_status

(* Clausal environments *)

type clbinding =
  | Cltyp of Name.t * constr freelisted
  | Clval of Name.t * (constr freelisted * instance_status) * constr freelisted

let map_clb f = function
  | Cltyp (na,cfl) -> Cltyp (na,map_fl f cfl)
  | Clval (na,(cfl1,pb),cfl2) -> Clval (na,(map_fl f cfl1,pb),map_fl f cfl2)

(* name of defined is erased (but it is pretty-printed) *)
let clb_name = function
    Cltyp(na,_) -> (na,false)
  | Clval (na,_,_) -> (na,true)

(***********************)

module Metaset = Int.Set

module Metamap = Int.Map

let metamap_to_list m =
  Metamap.fold (fun n v l -> (n,v)::l) m []

(*************************)
(* Unification state *)

type conv_pb = Reduction.conv_pb
type evar_constraint = conv_pb * Environ.env * constr * constr

module EvMap = Evar.Map

module EvNames :
sig

open Misctypes

type t

val empty : t
val add_name_newly_undefined : intro_pattern_naming_expr -> Evar.t -> evar_info -> t -> t
val add_name_undefined : intro_pattern_naming_expr -> Evar.t -> evar_info -> t -> t
val remove_name_defined : Evar.t -> t -> t
val rename : Evar.t -> Id.t -> t -> t
val reassign_name_defined : Evar.t -> Evar.t -> t -> t
val ident : Evar.t -> t -> Id.t option
val key : Id.t -> t -> Evar.t

end =
struct

type t = Id.t EvMap.t * existential_key Idmap.t

let empty = (EvMap.empty, Idmap.empty)

let add_name_newly_undefined naming evk evi (evtoid, idtoev as names) =
  let id = match naming with
  | Misctypes.IntroAnonymous -> None
  | Misctypes.IntroIdentifier id ->
    if Idmap.mem id idtoev then
    user_err_loc
      (Loc.ghost,"",str "Already an existential evar of name " ++ pr_id id);
    Some id
  | Misctypes.IntroFresh id ->
    let id = Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev) in
    Some id
  in
  match id with
  | None -> names
  | Some id -> (EvMap.add evk id evtoid, Idmap.add id evk idtoev)

let add_name_undefined naming evk evi (evtoid,idtoev as evar_names) =
  if EvMap.mem evk evtoid then
    evar_names
  else
    add_name_newly_undefined naming evk evi evar_names

let remove_name_defined evk (evtoid, idtoev as names) =
  let id = try Some (EvMap.find evk evtoid) with Not_found -> None in
  match id with
  | None -> names
  | Some id -> (EvMap.remove evk evtoid, Idmap.remove id idtoev)

let rename evk id (evtoid, idtoev) =
  let id' = try Some (EvMap.find evk evtoid) with Not_found -> None in
  match id' with
  | None -> (EvMap.add evk id evtoid, Idmap.add id evk idtoev)
  | Some id' ->
    if Idmap.mem id idtoev then anomaly (str "Evar name already in use");
    (EvMap.update evk id evtoid (* overwrite old name *), Idmap.add id evk (Idmap.remove id' idtoev))

let reassign_name_defined evk evk' (evtoid, idtoev as names) =
  let id = try Some (EvMap.find evk evtoid) with Not_found -> None in
  match id with
  | None -> names (** evk' must not be defined *)
  | Some id ->
    (EvMap.add evk' id (EvMap.remove evk evtoid),
    Idmap.add id evk' (Idmap.remove id idtoev))

let ident evk (evtoid, _) =
  try Some (EvMap.find evk evtoid) with Not_found -> None

let key id (_, idtoev) =
  Idmap.find id idtoev

end

type evar_map = {
  (** Existential variables *)
  defn_evars : evar_info EvMap.t;
  undf_evars : evar_info EvMap.t;
  evar_names : EvNames.t;
  (** Universes *)
  universes  : evar_universe_context;
  (** Conversion problems *)
  conv_pbs   : evar_constraint list;
  last_mods  : Evar.Set.t;
  (** Metas *)
  metas      : clbinding Metamap.t;
  (** Interactive proofs *)
  effects    : Safe_typing.private_constants;
  future_goals : Evar.t list; (** list of newly created evars, to be
                                  eventually turned into goals if not solved.*)
  principal_future_goal : Evar.t option; (** if [Some e], [e] must be
                                             contained
                                             [future_goals]. The evar
                                             [e] will inherit
                                             properties (now: the
                                             name) of the evar which
                                             will be instantiated with
                                             a term containing [e]. *)
  extras : Store.t;
}

(*** Lifting primitive from Evar.Map. ***)

let rename evk id evd =
  { evd with evar_names = EvNames.rename evk id evd.evar_names }

let add d e i = match i.evar_body with
| Evar_empty ->
  let evar_names = EvNames.add_name_undefined Misctypes.IntroAnonymous e i d.evar_names in
  { d with undf_evars = EvMap.add e i d.undf_evars; evar_names }
| Evar_defined _ ->
  let evar_names = EvNames.remove_name_defined e d.evar_names in
  { d with defn_evars = EvMap.add e i d.defn_evars; evar_names }

let remove d e =
  let undf_evars = EvMap.remove e d.undf_evars in
  let defn_evars = EvMap.remove e d.defn_evars in
  let principal_future_goal = match d.principal_future_goal with
  | None -> None
  | Some e' -> if Evar.equal e e' then None else d.principal_future_goal
  in
  let future_goals = List.filter (fun e' -> not (Evar.equal e e')) d.future_goals in
  { d with undf_evars; defn_evars; principal_future_goal; future_goals }

let find d e =
  try EvMap.find e d.undf_evars
  with Not_found -> EvMap.find e d.defn_evars

let find_undefined d e = EvMap.find e d.undf_evars

let mem d e = EvMap.mem e d.undf_evars || EvMap.mem e d.defn_evars

(* spiwack: this function loses information from the original evar_map
   it might be an idea not to export it. *)
let to_list d =
  (* Workaround for change in Map.fold behavior in ocaml 3.08.4 *)
  let l = ref [] in
  EvMap.iter (fun evk x -> l := (evk,x)::!l) d.defn_evars;
  EvMap.iter (fun evk x -> l := (evk,x)::!l) d.undf_evars;
  !l

let undefined_map d = d.undf_evars

let drop_all_defined d = { d with defn_evars = EvMap.empty }

(* spiwack: not clear what folding over an evar_map, for now we shall
    simply fold over the inner evar_map. *)
let fold f d a =
  EvMap.fold f d.defn_evars (EvMap.fold f d.undf_evars a)

let fold_undefined f d a = EvMap.fold f d.undf_evars a

let raw_map f d =
  let f evk info =
    let ans = f evk info in
    let () = match info.evar_body, ans.evar_body with
    | Evar_defined _, Evar_empty
    | Evar_empty, Evar_defined _ ->
      anomaly (str "Unrespectful mapping function.")
    | _ -> ()
    in
    ans
  in
  let defn_evars = EvMap.smartmapi f d.defn_evars in
  let undf_evars = EvMap.smartmapi f d.undf_evars in
  { d with defn_evars; undf_evars; }

let raw_map_undefined f d =
  let f evk info =
    let ans = f evk info in
    let () = match ans.evar_body with
    | Evar_defined _ ->
      anomaly (str "Unrespectful mapping function.")
    | _ -> ()
    in
    ans
  in
  { d with undf_evars = EvMap.smartmapi f d.undf_evars; }

let is_evar = mem

let is_defined d e = EvMap.mem e d.defn_evars

let is_undefined d e = EvMap.mem e d.undf_evars

let existential_value d (n, args) =
  let info = find d n in
  match evar_body info with
  | Evar_defined c ->
    instantiate_evar_array info c args
  | Evar_empty ->
    raise NotInstantiatedEvar

let existential_opt_value d ev =
  try Some (existential_value d ev)
  with NotInstantiatedEvar -> None

let existential_type d (n, args) =
  let info =
    try find d n
    with Not_found ->
      anomaly (str "Evar " ++ str (string_of_existential n) ++ str " was not declared") in
  instantiate_evar_array info info.evar_concl args

let add_constraints d c =
  { d with universes = add_constraints_context d.universes c }

let add_universe_constraints d c = 
  { d with universes = add_universe_constraints_context d.universes c }

(*** /Lifting... ***)

(* evar_map are considered empty disregarding histories *)
let is_empty d =
  EvMap.is_empty d.defn_evars &&
  EvMap.is_empty d.undf_evars &&
  List.is_empty d.conv_pbs &&
  Metamap.is_empty d.metas

let cmap f evd = 
  { evd with
      metas = Metamap.map (map_clb f) evd.metas;
      defn_evars = EvMap.map (map_evar_info f) evd.defn_evars;
      undf_evars = EvMap.map (map_evar_info f) evd.undf_evars
  }

(* spiwack: deprecated *)
let create_evar_defs sigma = { sigma with
  conv_pbs=[]; last_mods=Evar.Set.empty; metas=Metamap.empty }
(* spiwack: tentatively deprecated *)
let create_goal_evar_defs sigma = { sigma with
   (* conv_pbs=[]; last_mods=Evar.Set.empty; metas=Metamap.empty } *)
  metas=Metamap.empty } 

let empty = {
  defn_evars = EvMap.empty;
  undf_evars = EvMap.empty;
  universes  = empty_evar_universe_context;
  conv_pbs   = [];
  last_mods  = Evar.Set.empty;
  metas      = Metamap.empty;
  effects    = Safe_typing.empty_private_constants;
  evar_names = EvNames.empty; (* id<->key for undefined evars *)
  future_goals = [];
  principal_future_goal = None;
  extras = Store.empty;
}

let from_env e = 
  { empty with universes = evar_universe_context_from e }

let from_ctx ctx = { empty with universes = ctx }

let has_undefined evd = not (EvMap.is_empty evd.undf_evars)

let evars_reset_evd ?(with_conv_pbs=false) ?(with_univs=true) evd d =
  let conv_pbs = if with_conv_pbs then evd.conv_pbs else d.conv_pbs in
  let last_mods = if with_conv_pbs then evd.last_mods else d.last_mods in
  let universes = 
    if not with_univs then evd.universes
    else union_evar_universe_context evd.universes d.universes
  in
  { evd with
    metas = d.metas;
    last_mods; conv_pbs; universes }

let merge_universe_context evd uctx' =
  { evd with universes = union_evar_universe_context evd.universes uctx' }

let set_universe_context evd uctx' =
  { evd with universes = uctx' }

let add_conv_pb ?(tail=false) pb d =
  (** MS: we have duplicates here, why? *)
  if tail then {d with conv_pbs = d.conv_pbs @ [pb]}
  else {d with conv_pbs = pb::d.conv_pbs}

let evar_source evk d = (find d evk).evar_source

let evar_ident evk evd = EvNames.ident evk evd.evar_names
let evar_key id evd = EvNames.key id evd.evar_names

let define_aux def undef evk body =
  let oldinfo =
    try EvMap.find evk undef
    with Not_found ->
      if EvMap.mem evk def then
        anomaly ~label:"Evd.define" (Pp.str "cannot define an evar twice")
      else
        anomaly ~label:"Evd.define" (Pp.str "cannot define undeclared evar")
  in
  let () = assert (oldinfo.evar_body == Evar_empty) in
  let newinfo = { oldinfo with evar_body = Evar_defined body } in
  EvMap.add evk newinfo def, EvMap.remove evk undef

(* define the existential of section path sp as the constr body *)
let define evk body evd =
  let (defn_evars, undf_evars) = define_aux evd.defn_evars evd.undf_evars evk body in
  let last_mods = match evd.conv_pbs with
  | [] ->  evd.last_mods
  | _ -> Evar.Set.add evk evd.last_mods
  in
  let evar_names = EvNames.remove_name_defined evk evd.evar_names in
  { evd with defn_evars; undf_evars; last_mods; evar_names }

let evar_declare hyps evk ty ?(src=(Loc.ghost,Evar_kinds.InternalHole)) 
    ?(filter=Filter.identity) ?candidates ?(store=Store.empty)
    ?(naming=Misctypes.IntroAnonymous) evd =
  let () = match Filter.repr filter with
  | None -> ()
  | Some filter ->
    assert (Int.equal (List.length filter) (List.length (named_context_of_val hyps)))
  in
  let evar_info = {
    evar_hyps = hyps;
    evar_concl = ty;
    evar_body = Evar_empty;
    evar_filter = filter;
    evar_source = src;
    evar_candidates = candidates;
    evar_extra = store; }
  in
  let evar_names = EvNames.add_name_newly_undefined naming evk evar_info evd.evar_names in
  { evd with undf_evars = EvMap.add evk evar_info evd.undf_evars; evar_names }

let restrict evk evk' filter ?candidates evd =
  let evar_info = EvMap.find evk evd.undf_evars in
  let evar_info' =
    { evar_info with evar_filter = filter;
      evar_candidates = candidates;
      evar_extra = Store.empty } in
  let evar_names = EvNames.reassign_name_defined evk evk' evd.evar_names in
  let ctxt = Filter.filter_list filter (evar_context evar_info) in
  let id_inst = Array.map_of_list (fun (id,_,_) -> mkVar id) ctxt in
  let body = mkEvar(evk',id_inst) in
  let (defn_evars, undf_evars) = define_aux evd.defn_evars evd.undf_evars evk body in
  { evd with undf_evars = EvMap.add evk' evar_info' undf_evars;
    defn_evars; evar_names }

let downcast evk ccl evd =
  let evar_info = EvMap.find evk evd.undf_evars in
  let evar_info' = { evar_info with evar_concl = ccl } in
  { evd with undf_evars = EvMap.add evk evar_info' evd.undf_evars }

(* extracts conversion problems that satisfy predicate p *)
(* Note: conv_pbs not satisying p are stored back in reverse order *)
let extract_conv_pbs evd p =
  let (pbs,pbs1) =
    List.fold_left
      (fun (pbs,pbs1) pb ->
    	 if p pb then
	   (pb::pbs,pbs1)
         else
	   (pbs,pb::pbs1))
      ([],[])
      evd.conv_pbs
  in
  {evd with conv_pbs = pbs1; last_mods = Evar.Set.empty},
  pbs

let extract_changed_conv_pbs evd p =
  extract_conv_pbs evd (fun pb -> p evd.last_mods pb)

let extract_all_conv_pbs evd =
  extract_conv_pbs evd (fun _ -> true)

let loc_of_conv_pb evd (pbty,env,t1,t2) =
  match kind_of_term (fst (decompose_app t1)) with
  | Evar (evk1,_) -> fst (evar_source evk1 evd)
  | _ ->
  match kind_of_term (fst (decompose_app t2)) with
  | Evar (evk2,_) -> fst (evar_source evk2 evd)
  | _ -> Loc.ghost

(** The following functions return the set of evars immediately
    contained in the object *)

(* excluding defined evars *)

let evar_list c =
  let rec evrec acc c =
    match kind_of_term c with
    | Evar (evk, _ as ev) -> ev :: acc
    | _ -> fold_constr evrec acc c in
  evrec [] c

let evars_of_term c =
  let rec evrec acc c =
    match kind_of_term c with
    | Evar (n, l) -> Evar.Set.add n (Array.fold_left evrec acc l)
    | _ -> fold_constr evrec acc c
  in
  evrec Evar.Set.empty c

let evars_of_named_context nc =
  List.fold_right (fun (_, b, t) s ->
    Option.fold_left (fun s t ->
      Evar.Set.union s (evars_of_term t))
      (Evar.Set.union s (evars_of_term t)) b)
    nc Evar.Set.empty

let evars_of_filtered_evar_info evi =
  Evar.Set.union (evars_of_term evi.evar_concl)
    (Evar.Set.union
	(match evi.evar_body with
	| Evar_empty -> Evar.Set.empty
	| Evar_defined b -> evars_of_term b)
	(evars_of_named_context (evar_filtered_context evi)))

(**********************************************************)
(* Sort variables *)

type rigid = 
  | UnivRigid
  | UnivFlexible of bool (** Is substitution by an algebraic ok? *)

let univ_rigid = UnivRigid
let univ_flexible = UnivFlexible false
let univ_flexible_alg = UnivFlexible true

let evar_universe_context d = d.universes

let universe_context_set d = d.universes.uctx_local

let pr_uctx_level uctx = 
  let map, map_rev = uctx.uctx_names in 
    fun l ->
      try str(Univ.LMap.find l map_rev)
      with Not_found -> 
	Universes.pr_with_global_universes l

let universe_context ?names evd =
  match names with
  | None -> [], Univ.ContextSet.to_context evd.universes.uctx_local
  | Some pl ->
     let levels = Univ.ContextSet.levels evd.universes.uctx_local in
     let newinst, map, left =
       List.fold_right
         (fun (loc,id) (newinst, map, acc) ->
	  let l =
	    try UNameMap.find (Id.to_string id) (fst evd.universes.uctx_names)
	    with Not_found ->
	      user_err_loc (loc, "universe_context",
			    str"Universe " ++ pr_id id ++ str" is not bound anymore.")
	  in (l :: newinst, (id, l) :: map, Univ.LSet.remove l acc))
	 pl ([], [], levels)
     in
       if not (Univ.LSet.is_empty left) then
         let n = Univ.LSet.cardinal left in
           errorlabstrm "universe_context"
			(str(CString.plural n "Universe") ++ spc () ++
			     Univ.LSet.pr (pr_uctx_level evd.universes) left ++
			     spc () ++ str (CString.conjugate_verb_to_be n) ++ str" unbound.")
       else
	 let inst = Univ.Instance.of_array (Array.of_list newinst) in
	 let ctx = Univ.UContext.make (inst,
           Univ.ContextSet.constraints evd.universes.uctx_local)
	 in map, ctx

let restrict_universe_context evd vars =
  let uctx = evd.universes in
  let uctx' = Universes.restrict_universe_context uctx.uctx_local vars in
    { evd with universes = { uctx with uctx_local = uctx' } }
						 
let universe_subst evd =
  evd.universes.uctx_univ_variables

let merge_uctx sideff rigid uctx ctx' =
  let open Univ in
  let levels = ContextSet.levels ctx' in
  let uctx = if sideff then uctx else
    match rigid with
    | UnivRigid -> uctx
    | UnivFlexible b ->
      let fold u accu =
        if LMap.mem u accu then accu
        else LMap.add u None accu
      in
      let uvars' = LSet.fold fold levels uctx.uctx_univ_variables in
	if b then
	  { uctx with uctx_univ_variables = uvars';
	  uctx_univ_algebraic = LSet.union uctx.uctx_univ_algebraic levels }
	else { uctx with uctx_univ_variables = uvars' }
  in
  let uctx_local =
    if sideff then uctx.uctx_local
    else ContextSet.append ctx' uctx.uctx_local
  in
  let declare g =
    LSet.fold (fun u g ->
	       try Univ.add_universe u false g
	       with Univ.AlreadyDeclared when sideff -> g)
	      levels g
  in
  let initial = declare uctx.uctx_initial_universes in
  let univs = declare uctx.uctx_universes in
  let uctx_universes = merge_constraints (ContextSet.constraints ctx') univs in
    { uctx with uctx_local; uctx_universes; uctx_initial_universes = initial }

let merge_context_set ?(sideff=false) rigid evd ctx' = 
  {evd with universes = merge_uctx sideff rigid evd.universes ctx'}

let merge_uctx_subst uctx s =
  { uctx with uctx_univ_variables = Univ.LMap.subst_union uctx.uctx_univ_variables s }
      
let merge_universe_subst evd subst = 
  {evd with universes = merge_uctx_subst evd.universes subst }

let with_context_set rigid d (a, ctx) = 
  (merge_context_set rigid d ctx, a)

let emit_universe_side_effects eff u =
  let uctxs = Safe_typing.universes_of_private eff in
  List.fold_left (merge_uctx true univ_rigid) u uctxs
        
let uctx_new_univ_variable rigid name predicative
  ({ uctx_local = ctx; uctx_univ_variables = uvars; uctx_univ_algebraic = avars} as uctx) =
  let u = Universes.new_univ_level (Global.current_dirpath ()) in
  let ctx' = Univ.ContextSet.add_universe u ctx in
  let uctx', pred =
    match rigid with
    | UnivRigid -> uctx, true
    | UnivFlexible b -> 
      let uvars' = Univ.LMap.add u None uvars in
	if b then {uctx with uctx_univ_variables = uvars';
	  uctx_univ_algebraic = Univ.LSet.add u avars}, false
	else {uctx with uctx_univ_variables = uvars'}, false
  in
  let names = 
    match name with
    | Some n -> add_uctx_names n u uctx.uctx_names
    | None -> uctx.uctx_names
  in
  let initial =
    Univ.add_universe u false uctx.uctx_initial_universes
  in						     
  let uctx' =
    {uctx' with uctx_names = names; uctx_local = ctx';
		uctx_universes = Univ.add_universe u false uctx.uctx_universes;
		uctx_initial_universes = initial}
  in uctx', u
						     
let new_univ_level_variable ?name ?(predicative=true) rigid evd =
  let uctx', u = uctx_new_univ_variable rigid name predicative evd.universes in
    ({evd with universes = uctx'}, u)

let new_univ_variable ?name ?(predicative=true) rigid evd =
  let uctx', u = uctx_new_univ_variable rigid name predicative evd.universes in
    ({evd with universes = uctx'}, Univ.Universe.make u)

let new_sort_variable ?name ?(predicative=true) rigid d =
  let (d', u) = new_univ_variable rigid ?name ~predicative d in
    (d', Type u)

let add_global_univ d u =
  let uctx = d.universes in
  let initial =
    Univ.add_universe u true uctx.uctx_initial_universes
  in
  let univs = 
    Univ.add_universe u true uctx.uctx_universes
  in
    { d with universes = { uctx with uctx_local = Univ.ContextSet.add_universe u uctx.uctx_local;
				     uctx_initial_universes = initial;
				     uctx_universes = univs } }
      
let make_flexible_variable evd b u =
  let {uctx_univ_variables = uvars; uctx_univ_algebraic = avars} as ctx = evd.universes in
  let uvars' = Univ.LMap.add u None uvars in
  let avars' = 
    if b then
      let uu = Univ.Universe.make u in
      let substu_not_alg u' v =
	Option.cata (fun vu -> Univ.Universe.equal uu vu && not (Univ.LSet.mem u' avars)) false v
      in
	if not (Univ.LMap.exists substu_not_alg uvars)
	then Univ.LSet.add u avars else avars 
    else avars 
  in
    {evd with universes = {ctx with uctx_univ_variables = uvars'; 
      uctx_univ_algebraic = avars'}}

let make_evar_universe_context e l = 
  let uctx = evar_universe_context_from e in
    match l with
    | None -> uctx
    | Some us ->
       List.fold_left
	 (fun uctx (loc,id) ->
	  fst (uctx_new_univ_variable univ_rigid (Some (Id.to_string id)) true uctx))
	 uctx us
    
(****************************************)
(* Operations on constants              *)
(****************************************)

let fresh_sort_in_family ?(rigid=univ_flexible) env evd s = 
  with_context_set rigid evd (Universes.fresh_sort_in_family env s)

let fresh_constant_instance env evd c =
  with_context_set univ_flexible evd (Universes.fresh_constant_instance env c)

let fresh_inductive_instance env evd i =
  with_context_set univ_flexible evd (Universes.fresh_inductive_instance env i)

let fresh_constructor_instance env evd c =
  with_context_set univ_flexible evd (Universes.fresh_constructor_instance env c)

let fresh_global ?(rigid=univ_flexible) ?names env evd gr =
  with_context_set rigid evd (Universes.fresh_global_instance ?names env gr)

let whd_sort_variable evd t = t

let is_sort_variable evd s = 
  match s with 
  | Type u -> 
    (match Univ.universe_level u with
    | Some l as x -> 
      let uctx = evd.universes in
	if Univ.LSet.mem l (Univ.ContextSet.levels uctx.uctx_local) then x
	else None
    | None -> None)
  | _ -> None

let is_flexible_level evd l = 
  let uctx = evd.universes in
    Univ.LMap.mem l uctx.uctx_univ_variables

let is_eq_sort s1 s2 =
  if Sorts.equal s1 s2 then None
  else
    let u1 = univ_of_sort s1
    and u2 = univ_of_sort s2 in
      if Univ.Universe.equal u1 u2 then None
      else Some (u1, u2)

let normalize_universe evd =
  let vars = ref evd.universes.uctx_univ_variables in
  let normalize = Universes.normalize_universe_opt_subst vars in
    normalize

let normalize_universe_instance evd l =
  let vars = ref evd.universes.uctx_univ_variables in
  let normalize = Univ.level_subst_of (Universes.normalize_univ_variable_opt_subst vars) in
    Univ.Instance.subst_fn normalize l

let normalize_sort evars s =
  match s with
  | Prop _ -> s
  | Type u -> 
    let u' = normalize_universe evars u in
    if u' == u then s else Type u'

(* FIXME inefficient *)
let set_eq_sort env d s1 s2 =
  let s1 = normalize_sort d s1 and s2 = normalize_sort d s2 in
  match is_eq_sort s1 s2 with
  | None -> d
  | Some (u1, u2) ->
    if not (type_in_type env) then
      add_universe_constraints d
        (Universes.Constraints.singleton (u1,Universes.UEq,u2))
    else
      d

let has_lub evd u1 u2 =
  (* let normalize = Universes.normalize_universe_opt_subst (ref univs.uctx_univ_variables) in *)
  (* (\* let dref, norm = memo_normalize_universe d in *\) *)
  (* let u1 = normalize u1 and u2 = normalize u2 in *)
    if Univ.Universe.equal u1 u2 then evd
    else add_universe_constraints evd
      (Universes.Constraints.singleton (u1,Universes.ULub,u2))

let set_eq_level d u1 u2 =
  add_constraints d (Univ.enforce_eq_level u1 u2 Univ.Constraint.empty)

let set_leq_level d u1 u2 =
  add_constraints d (Univ.enforce_leq_level u1 u2 Univ.Constraint.empty)

let set_eq_instances ?(flex=false) d u1 u2 =
  add_universe_constraints d
    (Universes.enforce_eq_instances_univs flex u1 u2 Universes.Constraints.empty)

let set_leq_sort env evd s1 s2 =
  let s1 = normalize_sort evd s1 
  and s2 = normalize_sort evd s2 in
  match is_eq_sort s1 s2 with
  | None -> evd
  | Some (u1, u2) ->
    (* if Univ.is_type0_univ u2 then *)
    (*   if Univ.is_small_univ u1 then evd *)
    (*   else raise (Univ.UniverseInconsistency (Univ.Le, u1, u2, [])) *)
    (* else if Univ.is_type0m_univ u2 then  *)
    (*   raise (Univ.UniverseInconsistency (Univ.Le, u1, u2, [])) *)
    (* else  *)
      if not (type_in_type env) then
      add_universe_constraints evd (Universes.Constraints.singleton (u1,Universes.ULe,u2))
      else evd
	    
let check_eq evd s s' =
  Univ.check_eq evd.universes.uctx_universes s s'

let check_leq evd s s' =
  Univ.check_leq evd.universes.uctx_universes s s'

let subst_univs_context_with_def def usubst (ctx, cst) =
  (Univ.LSet.diff ctx def, Univ.subst_univs_constraints usubst cst)

let normalize_evar_universe_context_variables uctx =
  let normalized_variables, undef, def, subst = 
    Universes.normalize_univ_variables uctx.uctx_univ_variables 
  in
  let ctx_local = subst_univs_context_with_def def (Univ.make_subst subst) uctx.uctx_local in
  let ctx_local', univs = Universes.refresh_constraints uctx.uctx_initial_universes ctx_local in
    subst, { uctx with uctx_local = ctx_local';
      uctx_univ_variables = normalized_variables;
      uctx_universes = univs }

(* let normvarsconstrkey = Profile.declare_profile "normalize_evar_universe_context_variables";; *)
(* let normalize_evar_universe_context_variables = *)
(*   Profile.profile1 normvarsconstrkey normalize_evar_universe_context_variables;; *)
    
let abstract_undefined_variables uctx =
  let vars' = 
    Univ.LMap.fold (fun u v acc ->
      if v == None then Univ.LSet.remove u acc
      else acc)
    uctx.uctx_univ_variables uctx.uctx_univ_algebraic
  in { uctx with uctx_local = Univ.ContextSet.empty;
      uctx_univ_algebraic = vars' }

let fix_undefined_variables ({ universes = uctx } as evm) =
  let algs', vars' = 
    Univ.LMap.fold (fun u v (algs, vars as acc) ->
      if v == None then (Univ.LSet.remove u algs, Univ.LMap.remove u vars)
      else acc)
      uctx.uctx_univ_variables 
      (uctx.uctx_univ_algebraic, uctx.uctx_univ_variables)
  in
    {evm with universes = 
	{ uctx with uctx_univ_variables = vars';
	  uctx_univ_algebraic = algs' } }


let refresh_undefined_univ_variables uctx =
  let subst, ctx' = Universes.fresh_universe_context_set_instance uctx.uctx_local in
  let alg = Univ.LSet.fold (fun u acc -> Univ.LSet.add (Univ.subst_univs_level_level subst u) acc) 
    uctx.uctx_univ_algebraic Univ.LSet.empty 
  in
  let vars = 
    Univ.LMap.fold
      (fun u v acc ->
	Univ.LMap.add (Univ.subst_univs_level_level subst u) 
          (Option.map (Univ.subst_univs_level_universe subst) v) acc)
      uctx.uctx_univ_variables Univ.LMap.empty
  in
  let declare g = Univ.LSet.fold (fun u g -> Univ.add_universe u false g)
				   (Univ.ContextSet.levels ctx') g in
  let initial = declare uctx.uctx_initial_universes in
  let univs = declare Univ.initial_universes in
  let uctx' = {uctx_names = uctx.uctx_names;
	       uctx_local = ctx'; 
	       uctx_univ_variables = vars; uctx_univ_algebraic = alg;
	       uctx_universes = univs;
	       uctx_initial_universes = initial } in
    uctx', subst

let refresh_undefined_universes evd =
  let uctx', subst = refresh_undefined_univ_variables evd.universes in
  let evd' = cmap (subst_univs_level_constr subst) {evd with universes = uctx'} in
    evd', subst

let normalize_evar_universe_context uctx = 
  let rec fixpoint uctx = 
    let ((vars',algs'), us') = 
      Universes.normalize_context_set uctx.uctx_local uctx.uctx_univ_variables
        uctx.uctx_univ_algebraic
    in
      if Univ.ContextSet.equal us' uctx.uctx_local then uctx
      else
	let us', universes = Universes.refresh_constraints uctx.uctx_initial_universes us' in
	let uctx' = 
	  { uctx_names = uctx.uctx_names;
	    uctx_local = us'; 
	    uctx_univ_variables = vars'; 
	    uctx_univ_algebraic = algs';
	    uctx_universes = universes;
	    uctx_initial_universes = uctx.uctx_initial_universes }
	in fixpoint uctx'
  in fixpoint uctx

let nf_univ_variables evd = 
  let subst, uctx' = normalize_evar_universe_context_variables evd.universes in
  let evd' = {evd with universes = uctx'} in
    evd', subst

let nf_constraints evd =
  let subst, uctx' = normalize_evar_universe_context_variables evd.universes in
  let uctx' = normalize_evar_universe_context uctx' in
    {evd with universes = uctx'}

let nf_constraints = 
  if Flags.profile then
    let nfconstrkey = Profile.declare_profile "nf_constraints" in
      Profile.profile1 nfconstrkey nf_constraints
  else nf_constraints

let universe_of_name evd s = 
  UNameMap.find s (fst evd.universes.uctx_names)

let add_universe_name evd s l =
  let names' = add_uctx_names s l evd.universes.uctx_names in
    {evd with universes = {evd.universes with uctx_names = names'}}

let universes evd = evd.universes.uctx_universes

let update_sigma_env evd env =
  let univs = Environ.universes env in
  let eunivs =
    { evd.universes with uctx_initial_universes = univs;
			 uctx_universes = univs }
  in
  let eunivs = merge_uctx true univ_rigid eunivs eunivs.uctx_local in
  { evd with universes = eunivs }

(* Conversion w.r.t. an evar map and its local universes. *)

let test_conversion_gen env evd pb t u =
  match pb with 
  | Reduction.CONV -> 
    Reduction.trans_conv_universes 
      full_transparent_state ~evars:(existential_opt_value evd) env 
      evd.universes.uctx_universes t u
  | Reduction.CUMUL -> Reduction.trans_conv_leq_universes
     full_transparent_state ~evars:(existential_opt_value evd) env 
    evd.universes.uctx_universes t u

let test_conversion env d pb t u =
  try test_conversion_gen env d pb t u; true
  with _ -> false

let eq_constr_univs evd t u =
  let b, c = Universes.eq_constr_univs_infer evd.universes.uctx_universes t u in
    if b then 
      try let evd' = add_universe_constraints evd c in evd', b
      with Univ.UniverseInconsistency _ | UniversesDiffer -> evd, false
    else evd, b

let e_eq_constr_univs evdref t u =
  let evd, b = eq_constr_univs !evdref t u in
    evdref := evd; b

(**********************************************************)
(* Side effects *)

let emit_side_effects eff evd =
  { evd with effects = Safe_typing.concat_private eff evd.effects;
	     universes = emit_universe_side_effects eff evd.universes }

let drop_side_effects evd =
  { evd with effects = Safe_typing.empty_private_constants; }

let eval_side_effects evd = evd.effects

(* Future goals *)
let declare_future_goal evk evd =
  { evd with future_goals = evk::evd.future_goals }

let declare_principal_goal evk evd =
  match evd.principal_future_goal with
  | None -> { evd with
    future_goals = evk::evd.future_goals;
    principal_future_goal=Some evk; }
  | Some _ -> Errors.error "Only one main subgoal per instantiation."

let future_goals evd = evd.future_goals

let principal_future_goal evd = evd.principal_future_goal

let reset_future_goals evd =
  { evd with future_goals = [] ; principal_future_goal=None }

let restore_future_goals evd gls pgl =
  { evd with future_goals = gls ; principal_future_goal = pgl }

(**********************************************************)
(* Accessing metas *)

(** We use this function to overcome OCaml compiler limitations and to prevent
    the use of costly in-place modifications. *)
let set_metas evd metas = {
  defn_evars = evd.defn_evars;
  undf_evars = evd.undf_evars;
  universes  = evd.universes;
  conv_pbs = evd.conv_pbs;
  last_mods = evd.last_mods;
  metas;
  effects = evd.effects;
  evar_names = evd.evar_names;
  future_goals = evd.future_goals;
  principal_future_goal = evd.principal_future_goal;
  extras = evd.extras;
}

let meta_list evd = metamap_to_list evd.metas

let undefined_metas evd =
  let filter = function
    | (n,Clval(_,_,typ)) -> None
    | (n,Cltyp (_,typ))  -> Some n
  in
  let m = List.map_filter filter (meta_list evd) in
  List.sort Int.compare m

let map_metas_fvalue f evd =
  let map = function
  | Clval(id,(c,s),typ) -> Clval(id,(mk_freelisted (f c.rebus),s),typ)
  | x -> x
  in
  set_metas evd (Metamap.smartmap map evd.metas)

let map_metas f evd =
  let map cl = map_clb f cl in
  set_metas evd (Metamap.smartmap map evd.metas)

let meta_opt_fvalue evd mv =
  match Metamap.find mv evd.metas with
    | Clval(_,b,_) -> Some b
    | Cltyp _ -> None

let meta_defined evd mv =
  match Metamap.find mv evd.metas with
    | Clval _ -> true
    | Cltyp _ -> false

let try_meta_fvalue evd mv =
  match Metamap.find mv evd.metas with
    | Clval(_,b,_) -> b
    | Cltyp _ -> raise Not_found

let meta_fvalue evd mv =
  try try_meta_fvalue evd mv
  with Not_found -> anomaly ~label:"meta_fvalue" (Pp.str "meta has no value")

let meta_value evd mv =
  (fst (try_meta_fvalue evd mv)).rebus

let meta_ftype evd mv =
  match Metamap.find mv evd.metas with
    | Cltyp (_,b) -> b
    | Clval(_,_,b) -> b

let meta_type evd mv = (meta_ftype evd mv).rebus

let meta_declare mv v ?(name=Anonymous) evd =
  let metas = Metamap.add mv (Cltyp(name,mk_freelisted v)) evd.metas in
  set_metas evd metas

let meta_assign mv (v, pb) evd =
  let modify _ = function
  | Cltyp (na, ty) -> Clval (na, (mk_freelisted v, pb), ty)
  | _ -> anomaly ~label:"meta_assign" (Pp.str "already defined")
  in
  let metas = Metamap.modify mv modify evd.metas in
  set_metas evd metas

let meta_reassign mv (v, pb) evd =
  let modify _ = function
  | Clval(na, _, ty) -> Clval (na, (mk_freelisted v, pb), ty)
  | _ -> anomaly ~label:"meta_reassign" (Pp.str "not yet defined")
  in
  let metas = Metamap.modify mv modify evd.metas in
  set_metas evd metas

(* If the meta is defined then forget its name *)
let meta_name evd mv =
  try fst (clb_name (Metamap.find mv evd.metas)) with Not_found -> Anonymous

let explain_no_such_bound_variable evd id =
  let mvl =
    List.rev (Metamap.fold (fun n clb l ->
      let na = fst (clb_name clb) in
      if na != Anonymous then out_name na :: l else l)
    evd.metas []) in
  errorlabstrm "Evd.meta_with_name"
    (str"No such bound variable " ++ pr_id id ++
     (if mvl == [] then str " (no bound variables at all in the expression)."
      else
        (str" (possible name" ++
         str (if List.length mvl == 1 then " is: " else "s are: ") ++
         pr_enum pr_id mvl ++ str").")))

let meta_with_name evd id =
  let na = Name id in
  let (mvl,mvnodef) =
    Metamap.fold
      (fun n clb (l1,l2 as l) ->
        let (na',def) = clb_name clb in
        if Name.equal na na' then if def then (n::l1,l2) else (n::l1,n::l2)
        else l)
      evd.metas ([],[]) in
  match mvnodef, mvl with
    | _,[]  ->
      explain_no_such_bound_variable evd id
    | ([n],_|_,[n]) ->
	n
    | _  ->
	errorlabstrm "Evd.meta_with_name"
          (str "Binder name \"" ++ pr_id id ++
           strbrk "\" occurs more than once in clause.")

let clear_metas evd = {evd with metas = Metamap.empty}

let meta_merge ?(with_univs = true) evd1 evd2 =
  let metas = Metamap.fold Metamap.add evd1.metas evd2.metas in
  let universes =
    if with_univs then union_evar_universe_context evd2.universes evd1.universes
    else evd2.universes
  in
  {evd2 with universes; metas; }

type metabinding = metavariable * constr * instance_status

let retract_coercible_metas evd =
  let mc = ref [] in
  let map n v = match v with
  | Clval (na, (b, (Conv, CoerceToType as s)), typ) ->
    let () = mc := (n, b.rebus, s) :: !mc in
    Cltyp (na, typ)
  | v -> v
  in
  let metas = Metamap.smartmapi map evd.metas in
  !mc, set_metas evd metas

let subst_defined_metas_evars (bl,el) c =
  let rec substrec c = match kind_of_term c with
    | Meta i ->
      let select (j,_,_) = Int.equal i j in
      substrec (pi2 (List.find select bl))
    | Evar (evk,args) ->
      let select (_,(evk',args'),_) = Evar.equal evk evk' && Array.equal Constr.equal args args' in
      (try substrec (pi3 (List.find select el))
       with Not_found -> map_constr substrec c)
    | _ -> map_constr substrec c
  in try Some (substrec c) with Not_found -> None

let evar_source_of_meta mv evd =
  match meta_name evd mv with
  | Anonymous -> (Loc.ghost,Evar_kinds.GoalEvar)
  | Name id -> (Loc.ghost,Evar_kinds.VarInstance id)

let dependent_evar_ident ev evd =
  let evi = find evd ev in
  match evi.evar_source with
  | (_,Evar_kinds.VarInstance id) -> id
  | _ -> anomaly (str "Not an evar resulting of a dependent binding")

(**********************************************************)
(* Extra data *)

let get_extra_data evd = evd.extras
let set_extra_data extras evd = { evd with extras }

(*******************************************************************)

type pending = (* before: *) evar_map * (* after: *) evar_map

type pending_constr = pending * constr

type open_constr = evar_map * constr

(*******************************************************************)
(* The type constructor ['a sigma] adds an evar map to an object of
  type ['a] *)
type 'a sigma = {
  it : 'a ;
  sigma : evar_map
}

let sig_it x = x.it
let sig_sig x = x.sigma
let on_sig s f = 
  let sigma', v = f s.sigma in
    { s with sigma = sigma' }, v

(*******************************************************************)
(* The state monad with state an evar map. *)

module MonadR =
  Monad.Make (struct

    type +'a t = evar_map -> evar_map * 'a

    let return a = fun s -> (s,a)

    let (>>=) x f = fun s ->
      let (s',a) = x s in
      f a s'

    let (>>) x y = fun s ->
      let (s',()) = x s in
      y s'

    let map f x = fun s ->
      on_snd f (x s)

  end)

module Monad =
  Monad.Make (struct

    type +'a t = evar_map -> 'a * evar_map

    let return a = fun s -> (a,s)

    let (>>=) x f = fun s ->
      let (a,s') = x s in
      f a s'

    let (>>) x y = fun s ->
      let ((),s') = x s in
      y s'

    let map f x = fun s ->
      on_fst f (x s)

  end)

(**********************************************************)
(* Failure explanation *)

type unsolvability_explanation = SeveralInstancesFound of int

(**********************************************************)
(* Pretty-printing *)

let pr_evar_suggested_name evk sigma =
  let base_id evk' evi =
  match evar_ident evk' sigma with
  | Some id -> id
  | None -> match evi.evar_source with
  | _,Evar_kinds.ImplicitArg (c,(n,Some id),b) -> id
  | _,Evar_kinds.VarInstance id -> id
  | _,Evar_kinds.GoalEvar -> Id.of_string "Goal"
  | _ ->
      let env = reset_with_named_context evi.evar_hyps (Global.env()) in
      Namegen.id_of_name_using_hdchar env evi.evar_concl Anonymous
  in
  let names = EvMap.mapi base_id sigma.undf_evars in
  let id = EvMap.find evk names in
  let fold evk' id' (seen, n) =
    if seen then (seen, n)
    else if Evar.equal evk evk' then (true, n)
    else if Id.equal id id' then (seen, succ n)
    else (seen, n)
  in
  let (_, n) = EvMap.fold fold names (false, 0) in
  if n = 0 then id else Nameops.add_suffix id (string_of_int (pred n))

let pr_existential_key sigma evk = match evar_ident evk sigma with
| None ->
  str "?" ++ pr_id (pr_evar_suggested_name evk sigma)
| Some id ->
  str "?" ++ pr_id id

let pr_instance_status (sc,typ) =
  begin match sc with
  | IsSubType -> str " [or a subtype of it]"
  | IsSuperType -> str " [or a supertype of it]"
  | Conv -> mt ()
  end ++
  begin match typ with
  | CoerceToType -> str " [up to coercion]"
  | TypeNotProcessed -> mt ()
  | TypeProcessed -> str " [type is checked]"
  end

let pr_meta_map mmap =
  let pr_name = function
      Name id -> str"[" ++ pr_id id ++ str"]"
    | _ -> mt() in
  let pr_meta_binding = function
    | (mv,Cltyp (na,b)) ->
      	hov 0
	  (pr_meta mv ++ pr_name na ++ str " : " ++
           print_constr b.rebus ++ fnl ())
    | (mv,Clval(na,(b,s),t)) ->
      	hov 0
	  (pr_meta mv ++ pr_name na ++ str " := " ++
           print_constr b.rebus ++
	   str " : " ++ print_constr t.rebus ++
	   spc () ++ pr_instance_status s ++ fnl ())
  in
  prlist pr_meta_binding (metamap_to_list mmap)

let pr_decl ((id,b,_),ok) =
  match b with
  | None -> if ok then pr_id id else (str "{" ++ pr_id id ++ str "}")
  | Some c -> str (if ok then "(" else "{") ++ pr_id id ++ str ":=" ++
      print_constr c ++ str (if ok then ")" else "}")

let rec pr_evar_source = function
  | Evar_kinds.QuestionMark _ -> str "underscore"
  | Evar_kinds.CasesType false -> str "pattern-matching return predicate"
  | Evar_kinds.CasesType true ->
      str "subterm of pattern-matching return predicate"
  | Evar_kinds.BinderType (Name id) -> str "type of " ++ Nameops.pr_id id
  | Evar_kinds.BinderType Anonymous -> str "type of anonymous binder"
  | Evar_kinds.ImplicitArg (c,(n,ido),b) ->
      let id = Option.get ido in
      str "parameter " ++ pr_id id ++ spc () ++ str "of" ++
      spc () ++ print_constr (printable_constr_of_global c)
  | Evar_kinds.InternalHole -> str "internal placeholder"
  | Evar_kinds.TomatchTypeParameter (ind,n) ->
      pr_nth n ++ str " argument of type " ++ print_constr (mkInd ind)
  | Evar_kinds.GoalEvar -> str "goal evar"
  | Evar_kinds.ImpossibleCase -> str "type of impossible pattern-matching clause"
  | Evar_kinds.MatchingVar _ -> str "matching variable"
  | Evar_kinds.VarInstance id -> str "instance of " ++ pr_id id
  | Evar_kinds.SubEvar evk ->
      str "subterm of " ++ str (string_of_existential evk)

let pr_evar_info evi =
  let phyps =
    try
      let decls = match Filter.repr (evar_filter evi) with
      | None -> List.map (fun c -> (c, true)) (evar_context evi)
      | Some filter -> List.combine (evar_context evi) filter
      in
      prlist_with_sep spc pr_decl (List.rev decls)
    with Invalid_argument _ -> str "Ill-formed filtered context" in
  let pty = print_constr evi.evar_concl in
  let pb =
    match evi.evar_body with
      | Evar_empty -> mt ()
      | Evar_defined c -> spc() ++ str"=> "  ++ print_constr c
  in
  let candidates =
    match evi.evar_body, evi.evar_candidates with
      | Evar_empty, Some l ->
           spc () ++ str "{" ++
           prlist_with_sep (fun () -> str "|") print_constr l ++ str "}"
      | _ ->
          mt ()
  in
  let src = str "(" ++ pr_evar_source (snd evi.evar_source) ++ str ")" in
  hov 2
    (str"["  ++ phyps ++ spc () ++ str"|- "  ++ pty ++ pb ++ str"]" ++
       candidates ++ spc() ++ src)

let compute_evar_dependency_graph (sigma : evar_map) =
  (* Compute the map binding ev to the evars whose body depends on ev *)
  let fold evk evi acc =
    let fold_ev evk' acc =
      let tab =
        try EvMap.find evk' acc
        with Not_found -> Evar.Set.empty
      in
      EvMap.add evk' (Evar.Set.add evk tab) acc
    in
    match evar_body evi with
    | Evar_empty -> assert false
    | Evar_defined c -> Evar.Set.fold fold_ev (evars_of_term c) acc
  in
  EvMap.fold fold sigma.defn_evars EvMap.empty

let evar_dependency_closure n sigma =
  (** Create the DAG of depth [n] representing the recursive dependencies of
      undefined evars. *)
  let graph = compute_evar_dependency_graph sigma in
  let rec aux n curr accu =
    if Int.equal n 0 then Evar.Set.union curr accu
    else
      let fold evk accu =
        try
          let deps = EvMap.find evk graph in
          Evar.Set.union deps accu
        with Not_found -> accu
      in
      (** Consider only the newly added evars *)
      let ncurr = Evar.Set.fold fold curr Evar.Set.empty in
      (** Merge the others *)
      let accu = Evar.Set.union curr accu in
      aux (n - 1) ncurr accu
  in
  let undef = EvMap.domain (undefined_map sigma) in
  aux n undef Evar.Set.empty

let evar_dependency_closure n sigma =
  let deps = evar_dependency_closure n sigma in
  let map = EvMap.bind (fun ev -> find sigma ev) deps in
  EvMap.bindings map

let has_no_evar sigma =
  EvMap.is_empty sigma.defn_evars && EvMap.is_empty sigma.undf_evars

let pr_evd_level evd = pr_uctx_level evd.universes

let pr_evar_universe_context ctx =
  let prl = pr_uctx_level ctx in
  if is_empty_evar_universe_context ctx then mt ()
  else
    (str"UNIVERSES:"++brk(0,1)++ 
       h 0 (Univ.pr_universe_context_set prl ctx.uctx_local) ++ fnl () ++
     str"ALGEBRAIC UNIVERSES:"++brk(0,1)++
     h 0 (Univ.LSet.pr prl ctx.uctx_univ_algebraic) ++ fnl() ++
     str"UNDEFINED UNIVERSES:"++brk(0,1)++
       h 0 (Universes.pr_universe_opt_subst ctx.uctx_univ_variables) ++ fnl())

let print_env_short env =
  let pr_body n = function
  | None -> pr_name n
  | Some b -> str "(" ++ pr_name n ++ str " := " ++ print_constr b ++ str ")" in
  let pr_named_decl (n, b, _) = pr_body (Name n) b in
  let pr_rel_decl (n, b, _) = pr_body n b in
  let nc = List.rev (named_context env) in
  let rc = List.rev (rel_context env) in
    str "[" ++ pr_sequence pr_named_decl nc ++ str "]" ++ spc () ++
    str "[" ++ pr_sequence pr_rel_decl rc ++ str "]"

let pr_evar_constraints pbs =
  let pr_evconstr (pbty, env, t1, t2) =
    let env =
      (** We currently allow evar instances to refer to anonymous de
          Bruijn indices, so we protect the error printing code in this
          case by giving names to every de Bruijn variable in the
          rel_context of the conversion problem. MS: we should rather
          stop depending on anonymous variables, they can be used to
          indicate independency. Also, this depends on a strategy for
          naming/renaming. *)
      Namegen.make_all_name_different env
    in
    print_env_short env ++ spc () ++ str "|-" ++ spc () ++
      print_constr_env env t1 ++ spc () ++
      str (match pbty with
            | Reduction.CONV -> "=="
            | Reduction.CUMUL -> "<=") ++
      spc () ++ print_constr_env env t2
  in
  prlist_with_sep fnl pr_evconstr pbs

let pr_evar_map_gen with_univs pr_evars sigma =
  let { universes = uvs } = sigma in
  let evs = if has_no_evar sigma then mt () else pr_evars sigma ++ fnl ()
  and svs = if with_univs then pr_evar_universe_context uvs else mt ()
  and cstrs =
    if List.is_empty sigma.conv_pbs then mt ()
    else
    str "CONSTRAINTS:" ++ brk (0, 1) ++
      pr_evar_constraints sigma.conv_pbs ++ fnl ()
  and metas =
    if Metamap.is_empty sigma.metas then mt ()
    else
      str "METAS:" ++ brk (0, 1) ++ pr_meta_map sigma.metas
  in
  evs ++ svs ++ cstrs ++ metas

let pr_evar_list sigma l =
  let pr (ev, evi) =
    h 0 (str (string_of_existential ev) ++
      str "==" ++ pr_evar_info evi ++
      (if evi.evar_body == Evar_empty
       then str " {" ++  pr_existential_key sigma ev ++ str "}"
       else mt ()))
  in
  h 0 (prlist_with_sep fnl pr l)

let pr_evar_by_depth depth sigma = match depth with
| None ->
  (* Print all evars *)
  str"EVARS:"++brk(0,1)++pr_evar_list sigma (to_list sigma)++fnl()
| Some n ->
  (* Print all evars *)
  str"UNDEFINED EVARS:"++
  (if Int.equal n 0 then mt() else str" (+level "++int n++str" closure):")++
  brk(0,1)++
  pr_evar_list sigma (evar_dependency_closure n sigma)++fnl()

let pr_evar_by_filter filter sigma =
  let defined = Evar.Map.filter filter sigma.defn_evars in
  let undefined = Evar.Map.filter filter sigma.undf_evars in
  let prdef =
    if Evar.Map.is_empty defined then mt ()
    else str "DEFINED EVARS:" ++ brk (0, 1) ++
      pr_evar_list sigma (Evar.Map.bindings defined)
  in
  let prundef =
    if Evar.Map.is_empty undefined then mt ()
    else str "UNDEFINED EVARS:" ++ brk (0, 1) ++
      pr_evar_list sigma (Evar.Map.bindings undefined)
  in
  prdef ++ prundef

let pr_evar_map ?(with_univs=true) depth sigma =
  pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_depth depth sigma) sigma

let pr_evar_map_filter ?(with_univs=true) filter sigma =
  pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_filter filter sigma) sigma

let pr_metaset metas =
  str "[" ++ pr_sequence pr_meta (Metaset.elements metas) ++ str "]"