Adding a new folder corresponding to the low-level part of the pretyper

together with the tactic monad.

The move is not complete yet, because some file candidates for this directory
have almost useless dependencies in other ones that should not be moved.

9 files changed, 4619 insertions, 0 deletions

diff --git a/engine/engine.mllib b/engine/engine.mllib
new file mode 100644
index 000000000..4073f7e44
--- /dev/null
+++ b/engine/engine.mllib
@@ -0,0 +1,4 @@
+Logic_monad
+Termops
+Namegen
+Evd
diff --git a/engine/evd.ml b/engine/evd.ml
new file mode 100644
index 000000000..454c51195
--- /dev/null
+++ b/engine/evd.ml
@@ -0,0 +1,1769 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \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 }
+
+let evar_ident_info evi =
+  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
+
+(* 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 types 
+	and universe instances 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 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 = 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 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 ctx = ctx.uctx_local
+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 instantiate_variable l b v =
+  (* let b = Univ.subst_large_constraint (Univ.Universe.make l) Univ.type0m_univ b in *)
+  (* if Univ.univ_depends (Univ.Universe.make l) b then  *)
+  (*   error ("Occur-check in universe variable instantiation") *)
+  (* else *) 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
+			Univ.enforce_eq (Univ.Universe.make l) 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
+           | _, _ (* 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 cstrs 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
+
+type evar_map = {
+  (** Existential variables *)
+  defn_evars : evar_info EvMap.t;
+  undf_evars : evar_info EvMap.t;
+  evar_names : Id.t EvMap.t * existential_key Idmap.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    : Declareops.side_effects;
+  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]. *)
+}
+
+(*** Lifting primitive from Evar.Map. ***)
+
+let add_name_newly_undefined naming evk evi (evtoid,idtoev) =
+  let id = match naming with
+  | Misctypes.IntroAnonymous ->
+      let id = evar_ident_info evi in
+      Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev)
+  | Misctypes.IntroIdentifier id ->
+      let id' =
+        Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev) in
+      if not (Names.Id.equal id id') then
+        user_err_loc
+          (Loc.ghost,"",str "Already an existential evar of name " ++ pr_id id);
+      id'
+  | Misctypes.IntroFresh id ->
+      Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev) in
+  (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) =
+  let id = EvMap.find evk evtoid in
+  (EvMap.remove evk evtoid, Idmap.remove id idtoev)
+
+let remove_name_possibly_already_defined evk evar_names =
+  try remove_name_defined evk evar_names
+  with Not_found -> evar_names
+
+let rename evk id evd =
+  let (evtoid,idtoev) = evd.evar_names in
+  let id' = EvMap.find evk evtoid in
+  if Idmap.mem id idtoev then anomaly (str "Evar name already in use");
+  { evd with evar_names =
+      (EvMap.add evk id evtoid (* overwrite old name *),
+       Idmap.add id evk (Idmap.remove id' idtoev)) }
+
+let reassign_name_defined evk evk' (evtoid,idtoev) =
+  let id = EvMap.find evk evtoid in
+  (EvMap.add evk' id (EvMap.remove evk evtoid),
+   Idmap.add id evk' (Idmap.remove id idtoev))
+
+let add d e i = match i.evar_body with
+| Evar_empty ->
+  let evar_names = 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 = remove_name_possibly_already_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
+  { d with undf_evars; defn_evars; }
+
+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.defn_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    = Declareops.no_seff;
+  evar_names = (EvMap.empty,Idmap.empty); (* id<->key for undefined evars *)
+  future_goals = [];
+  principal_future_goal = None;
+}
+
+let from_env ?ctx e = 
+  match ctx with
+  | None -> { empty with universes = evar_universe_context_from e }
+  | Some 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 =
+  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 =
+  try EvMap.find evk (fst evd.evar_names)
+  with Not_found ->
+    (* Unnamed (non-dependent) evar *)
+    add_suffix (Id.of_string "X") (string_of_int (Evar.repr evk))
+
+let evar_key id evd =
+  Idmap.find id (snd 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 = 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 = 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 = 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)))
+
+(**********************************************************)
+(* Side effects *)
+
+let emit_side_effects eff evd =
+  { evd with effects = Declareops.union_side_effects eff evd.effects; }
+
+let drop_side_effects evd =
+  { evd with effects = Declareops.no_seff; }
+
+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 }
+
+(**********************************************************)
+(* 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 universe_context evd =
+  Univ.ContextSet.to_context evd.universes.uctx_local
+
+let universe_subst evd =
+  evd.universes.uctx_univ_variables
+
+let merge_uctx rigid uctx ctx' =
+  let open Univ in
+  let uctx = 
+    match rigid with
+    | UnivRigid -> uctx
+    | UnivFlexible b ->
+      let levels = ContextSet.levels ctx' in
+      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 = ContextSet.append ctx' uctx.uctx_local in
+  let uctx_universes = merge_constraints (ContextSet.constraints ctx') uctx.uctx_universes in
+  { uctx with uctx_local; uctx_universes }
+
+let merge_context_set rigid evd ctx' = 
+  {evd with universes = merge_uctx 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 add_uctx_names s l (names, names_rev) =
+    (UNameMap.add s l names, Univ.LMap.add l s names_rev)
+
+let uctx_new_univ_variable rigid name
+  ({ 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' = 
+    match rigid with
+    | UnivRigid -> uctx
+    | 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}
+	else {uctx with uctx_univ_variables = Univ.LMap.add u None uvars} in
+  let names = 
+    match name with
+    | Some n -> add_uctx_names n u uctx.uctx_names
+    | None -> uctx.uctx_names
+  in
+    {uctx' with uctx_names = names; uctx_local = ctx';
+      uctx_universes = Univ.add_universe u uctx.uctx_universes}, u
+
+let new_univ_level_variable ?name rigid evd =
+  let uctx', u = uctx_new_univ_variable rigid name evd.universes in
+    ({evd with universes = uctx'}, u)
+
+let new_univ_variable ?name rigid evd =
+  let uctx', u = uctx_new_univ_variable rigid name evd.universes in
+    ({evd with universes = uctx'}, Univ.Universe.make u)
+
+let new_sort_variable ?name rigid d =
+  let (d', u) = new_univ_variable rigid ?name d in
+    (d', Type u)
+
+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'}}
+
+(****************************************)
+(* 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 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 uctx' = {uctx_names = uctx.uctx_names;
+	       uctx_local = ctx'; 
+	       uctx_univ_variables = vars; uctx_univ_algebraic = alg;
+	       uctx_universes = Univ.initial_universes;
+	       uctx_initial_universes = uctx.uctx_initial_universes } 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.LSet.equal (fst us') (fst 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
+
+(* Conversion w.r.t. an evar map and its local universes. *)
+
+let 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 conversion_gen_key = Profile.declare_profile "conversion_gen" *)
+(* let conversion_gen = Profile.profile5 conversion_gen_key conversion_gen *)
+
+let conversion env d pb t u =
+  conversion_gen env d pb t u; d
+
+let test_conversion env d pb t u =
+  try 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
+
+let eq_constr_univs_test evd t u =
+  snd (eq_constr_univs evd t u)
+
+(**********************************************************)
+(* 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;
+}
+
+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 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 evd1 evd2 =
+  let metas = Metamap.fold Metamap.add evd1.metas evd2.metas in
+  let universes = union_evar_universe_context evd2.universes evd1.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")
+
+(*******************************************************************)
+
+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_existential_key sigma evk = str "?" ++ pr_id (evar_ident evk sigma)
+
+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_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 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) =
+    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_id (evar_ident ev sigma) ++ 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 "]"
diff --git a/engine/evd.mli b/engine/evd.mli
new file mode 100644
index 000000000..0765b951f
--- /dev/null
+++ b/engine/evd.mli
@@ -0,0 +1,600 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Util
+open Loc
+open Names
+open Term
+open Context
+open Environ
+
+(** {5 Existential variables and unification states}
+
+    A unification state (of type [evar_map]) is primarily a finite mapping
+    from existential variables to records containing the type of the evar
+    ([evar_concl]), the context under which it was introduced ([evar_hyps])
+    and its definition ([evar_body]). [evar_extra] is used to add any other
+    kind of information.
+
+    It also contains conversion constraints, debugging information and
+    information about meta variables. *)
+
+(** {6 Evars} *)
+
+type evar = existential_key
+(** Existential variables. TODO: Should be made opaque one day. *)
+
+val string_of_existential : evar -> string
+
+(** {6 Evar filters} *)
+
+module Filter :
+sig
+  type t
+  (** Evar filters, seen as bitmasks. *)
+
+  val equal : t -> t -> bool
+  (** Equality over filters *)
+
+  val identity : t
+  (** The identity filter. *)
+
+  val filter_list : t -> 'a list -> 'a list
+  (** Filter a list. Sizes must coincide. *)
+
+  val filter_array : t -> 'a array -> 'a array
+  (** Filter an array. Sizes must coincide. *)
+
+  val extend : int -> t -> t
+  (** [extend n f] extends [f] on the left with [n]-th times [true]. *)
+
+  val compose : t -> t -> t
+  (** Horizontal composition : [compose f1 f2] only keeps parts of [f2] where
+      [f1] is set. In particular, [f1] and [f2] must have the same length. *)
+
+  val apply_subfilter : t -> bool list -> t
+  (** [apply_subfilter f1 f2] applies filter [f2] where [f1] is [true]. In
+      particular, the length of [f2] is the number of times [f1] is [true] *)
+
+  val restrict_upon : t -> int -> (int -> bool) -> t option
+  (** Ad-hoc primitive. *)
+
+  val map_along : (bool -> 'a -> bool) -> t -> 'a list -> t
+  (** Apply the function on the filter and the list. Sizes must coincide. *)
+
+  val make : bool list -> t
+  (** Create out of a list *)
+
+  val repr :  t -> bool list option
+  (** Observe as a bool list. *)
+
+end
+
+(** {6 Evar infos} *)
+
+type evar_body =
+  | Evar_empty
+  | Evar_defined of constr
+
+
+module Store : Store.S
+(** Datatype used to store additional information in evar maps. *)
+
+type evar_info = {
+  evar_concl : constr;
+  (** Type of the evar. *)
+  evar_hyps : named_context_val;
+  (** Context of the evar. *)
+  evar_body : evar_body;
+  (** Optional content of the evar. *)
+  evar_filter : Filter.t;
+  (** Boolean mask over {!evar_hyps}. Should have the same length.
+      TODO: document me more. *)
+  evar_source : Evar_kinds.t located;
+  (** Information about the evar. *)
+  evar_candidates : constr list option;
+  (** TODO: document this *)
+  evar_extra : Store.t
+  (** Extra store, used for clever hacks. *)
+}
+
+val make_evar : named_context_val -> types -> evar_info
+val evar_concl : evar_info -> constr
+val evar_context : evar_info -> named_context
+val evar_filtered_context : evar_info -> named_context
+val evar_hyps : evar_info -> named_context_val
+val evar_filtered_hyps : evar_info -> named_context_val
+val evar_body : evar_info -> evar_body
+val evar_filter : evar_info -> Filter.t
+val evar_env :  evar_info -> env
+val evar_filtered_env :  evar_info -> env
+
+val map_evar_body : (constr -> constr) -> evar_body -> evar_body
+val map_evar_info : (constr -> constr) -> evar_info -> evar_info
+
+(** {6 Unification state} **)
+
+type evar_universe_context
+(** The universe context associated to an evar map *)
+
+type evar_map
+(** Type of unification state. Essentially a bunch of state-passing data needed
+    to handle incremental term construction. *)
+
+val empty : evar_map
+(** The empty evar map. *)
+
+val from_env : ?ctx:evar_universe_context -> env -> evar_map
+(** The empty evar map with given universe context, taking its initial 
+    universes from env. *)
+
+val is_empty : evar_map -> bool
+(** Whether an evarmap is empty. *)
+
+val has_undefined : evar_map -> bool
+(** [has_undefined sigma] is [true] if and only if
+    there are uninstantiated evars in [sigma]. *)
+
+val add : evar_map -> evar -> evar_info -> evar_map
+(** [add sigma ev info] adds [ev] with evar info [info] in sigma.
+    Precondition: ev must not preexist in [sigma]. *)
+
+val find : evar_map -> evar -> evar_info
+(** Recover the data associated to an evar. *)
+
+val find_undefined : evar_map -> evar -> evar_info
+(** Same as {!find} but restricted to undefined evars. For efficiency
+    reasons. *)
+
+val remove : evar_map -> evar -> evar_map
+(** Remove an evar from an evar map. Use with caution. *)
+
+val mem : evar_map -> evar -> bool
+(** Whether an evar is present in an evarmap. *)
+
+val fold : (evar -> evar_info -> 'a -> 'a) -> evar_map -> 'a -> 'a
+(** Apply a function to all evars and their associated info in an evarmap. *)
+
+val fold_undefined : (evar -> evar_info -> 'a -> 'a) -> evar_map -> 'a -> 'a
+(** Same as {!fold}, but restricted to undefined evars. For efficiency
+    reasons. *)
+
+val raw_map : (evar -> evar_info -> evar_info) -> evar_map -> evar_map
+(** Apply the given function to all evars in the map. Beware: this function
+    expects the argument function to preserve the kind of [evar_body], i.e. it
+    must send [Evar_empty] to [Evar_empty] and [Evar_defined c] to some
+    [Evar_defined c']. *)
+
+val raw_map_undefined : (evar -> evar_info -> evar_info) -> evar_map -> evar_map
+(** Same as {!raw_map}, but restricted to undefined evars. For efficiency
+    reasons. *)
+
+val define : evar -> constr -> evar_map -> evar_map
+(** Set the body of an evar to the given constr. It is expected that:
+    {ul
+      {- The evar is already present in the evarmap.}
+      {- The evar is not defined in the evarmap yet.}
+      {- All the evars present in the constr should be present in the evar map.}
+    } *)
+
+val cmap : (constr -> constr) -> evar_map -> evar_map
+(** Map the function on all terms in the evar map. *)
+
+val is_evar : evar_map -> evar -> bool
+(** Alias for {!mem}. *)
+
+val is_defined : evar_map -> evar -> bool
+(** Whether an evar is defined in an evarmap. *)
+
+val is_undefined : evar_map -> evar -> bool
+(** Whether an evar is not defined in an evarmap. *)
+
+val add_constraints : evar_map -> Univ.constraints -> evar_map
+(** Add universe constraints in an evar map. *)
+
+val undefined_map : evar_map -> evar_info Evar.Map.t
+(** Access the undefined evar mapping directly. *)
+
+val drop_all_defined : evar_map -> evar_map
+
+(** {6 Instantiating partial terms} *)
+
+exception NotInstantiatedEvar
+
+val existential_value : evar_map -> existential -> constr
+(** [existential_value sigma ev] raises [NotInstantiatedEvar] if [ev] has
+    no body and [Not_found] if it does not exist in [sigma] *)
+
+val existential_type : evar_map -> existential -> types
+
+val existential_opt_value : evar_map -> existential -> constr option
+(** Same as {!existential_value} but returns an option instead of raising an
+    exception. *)
+
+val evar_instance_array : (named_declaration -> 'a -> bool) -> evar_info ->
+  'a array -> (Id.t * 'a) list
+
+val instantiate_evar_array : evar_info -> constr -> constr array -> constr
+
+val evars_reset_evd  : ?with_conv_pbs:bool -> ?with_univs:bool -> 
+  evar_map ->  evar_map -> evar_map
+(** spiwack: this function seems to somewhat break the abstraction. *)
+
+(** {6 Misc} *)
+
+val evar_declare :
+  named_context_val -> evar -> types -> ?src:Loc.t * Evar_kinds.t ->
+      ?filter:Filter.t -> ?candidates:constr list -> ?store:Store.t ->
+      ?naming:Misctypes.intro_pattern_naming_expr -> evar_map -> evar_map
+(** Convenience function. Just a wrapper around {!add}. *)
+
+val restrict : evar -> evar -> Filter.t -> ?candidates:constr list ->
+  evar_map -> evar_map
+(** Restrict an undefined evar into a new evar by filtering context and
+    possibly limiting the instances to a set of candidates *)
+
+val downcast : evar -> types -> evar_map -> evar_map
+(** Change the type of an undefined evar to a new type assumed to be a
+    subtype of its current type; subtyping must be ensured by caller *)
+
+val evar_source : existential_key -> evar_map -> Evar_kinds.t located
+(** Convenience function. Wrapper around {!find} to recover the source of an
+    evar in a given evar map. *)
+
+val evar_ident : existential_key -> evar_map -> Id.t
+
+val rename : existential_key -> Id.t -> evar_map -> evar_map
+
+val evar_key : Id.t -> evar_map -> existential_key
+
+val evar_source_of_meta : metavariable -> evar_map -> Evar_kinds.t located
+
+val dependent_evar_ident : existential_key -> evar_map -> Id.t
+
+(** {5 Side-effects} *)
+
+val emit_side_effects : Declareops.side_effects -> evar_map -> evar_map
+(** Push a side-effect into the evar map. *)
+
+val eval_side_effects : evar_map -> Declareops.side_effects
+(** Return the effects contained in the evar map. *)
+
+val drop_side_effects : evar_map -> evar_map
+(** This should not be used. For hacking purposes. *)
+
+(** {5 Future goals} *)
+
+val declare_future_goal : Evar.t -> evar_map -> evar_map
+(** Adds an existential variable to the list of future goals. For
+    internal uses only. *)
+
+val declare_principal_goal : Evar.t -> evar_map -> evar_map
+(** Adds an existential variable to the list of future goals and make
+    it principal. Only one existential variable can be made principal, an
+    error is raised otherwise. For internal uses only. *)
+
+val future_goals : evar_map -> Evar.t list
+(** Retrieves the list of future goals. Used by the [refine] primitive
+    of the tactic engine. *)
+
+val principal_future_goal : evar_map -> Evar.t option
+(** Retrieves the name of the principal existential variable if there
+    is one. Used by the [refine] primitive of the tactic engine. *)
+
+val reset_future_goals : evar_map -> evar_map
+(** Clears the list of future goals (as well as the principal future
+    goal). Used by the [refine] primitive of the tactic engine. *)
+
+val restore_future_goals : evar_map -> Evar.t list -> Evar.t option -> evar_map
+(** Sets the future goals (including the principal future goal) to a
+    previous value. Intended to be used after a local list of future
+    goals has been consumed. Used by the [refine] primitive of the
+    tactic engine. *)
+
+(** {5 Sort variables}
+
+    Evar maps also keep track of the universe constraints defined at a given
+    point. This section defines the relevant manipulation functions. *)
+
+val whd_sort_variable : evar_map -> constr -> constr
+
+exception UniversesDiffer
+
+val add_universe_constraints : evar_map -> Universes.universe_constraints -> evar_map
+(** Add the given universe unification constraints to the evar map.
+    @raises UniversesDiffer in case a first-order unification fails.
+    @raises UniverseInconsistency
+*)
+(** {5 Enriching with evar maps} *)
+
+type 'a sigma = {
+  it : 'a ;
+  (** The base object. *)
+  sigma : evar_map
+  (** The added unification state. *)
+}
+(** The type constructor ['a sigma] adds an evar map to an object of type
+    ['a]. *)
+
+val sig_it  : 'a sigma -> 'a
+val sig_sig : 'a sigma -> evar_map
+val on_sig : 'a sigma -> (evar_map -> evar_map * 'b) -> 'a sigma * 'b
+
+(** {5 The state monad with state an evar map} *)
+
+module MonadR : Monad.S with type +'a t = evar_map -> evar_map * 'a
+module Monad  : Monad.S with type +'a t = evar_map -> 'a * evar_map
+
+
+(** {5 Meta machinery}
+
+    These functions are almost deprecated. They were used before the
+    introduction of the full-fledged evar calculus. In an ideal world, they
+    should be removed. Alas, some parts of the code still use them. Do not use
+    in newly-written code. *)
+
+module Metaset : Set.S with type elt = metavariable
+module Metamap : Map.ExtS with type key = metavariable and module Set := Metaset
+
+type 'a freelisted = {
+  rebus : 'a;
+  freemetas : Metaset.t }
+
+val metavars_of : constr -> Metaset.t
+val mk_freelisted : constr -> constr freelisted
+val map_fl : ('a -> 'b) -> 'a freelisted -> 'b freelisted
+
+(** 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
+
+val eq_instance_constraint :
+  instance_constraint -> instance_constraint -> bool
+
+(** 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
+
+(** Unification constraints *)
+type conv_pb = Reduction.conv_pb
+type evar_constraint = conv_pb * env * constr * constr
+val add_conv_pb : ?tail:bool -> evar_constraint -> evar_map -> evar_map
+
+val extract_changed_conv_pbs : evar_map ->
+      (Evar.Set.t -> evar_constraint -> bool) ->
+      evar_map * evar_constraint list
+val extract_all_conv_pbs : evar_map -> evar_map * evar_constraint list
+val loc_of_conv_pb : evar_map -> evar_constraint -> Loc.t
+
+(** The following functions return the set of evars immediately
+    contained in the object; need the term to be evar-normal otherwise
+    defined evars are returned too. *)
+
+val evar_list : constr -> existential list
+  (** excluding evars in instances of evars and collected with
+     redundancies from right to left (used by tactic "instantiate") *)
+
+val evars_of_term : constr -> Evar.Set.t
+  (** including evars in instances of evars *)
+
+val evars_of_named_context : named_context -> Evar.Set.t
+
+val evars_of_filtered_evar_info : evar_info -> Evar.Set.t
+
+(** Metas *)
+val meta_list : evar_map -> (metavariable * clbinding) list
+val meta_defined : evar_map -> metavariable -> bool
+
+val meta_value     : evar_map -> metavariable -> constr
+(** [meta_fvalue] raises [Not_found] if meta not in map or [Anomaly] if
+   meta has no value *)
+
+val meta_fvalue    : evar_map -> metavariable -> constr freelisted * instance_status
+val meta_opt_fvalue : evar_map -> metavariable -> (constr freelisted * instance_status) option
+val meta_type      : evar_map -> metavariable -> types
+val meta_ftype     : evar_map -> metavariable -> types freelisted
+val meta_name      : evar_map -> metavariable -> Name.t
+val meta_with_name : evar_map -> Id.t -> metavariable
+val meta_declare   :
+  metavariable -> types -> ?name:Name.t -> evar_map -> evar_map
+val meta_assign    : metavariable -> constr * instance_status -> evar_map -> evar_map
+val meta_reassign  : metavariable -> constr * instance_status -> evar_map -> evar_map
+
+val clear_metas : evar_map -> evar_map
+
+(** [meta_merge evd1 evd2] returns [evd2] extended with the metas of [evd1] *)
+val meta_merge : evar_map -> evar_map -> evar_map
+
+val undefined_metas : evar_map -> metavariable list
+val map_metas_fvalue : (constr -> constr) -> evar_map -> evar_map
+
+type metabinding = metavariable * constr * instance_status
+
+val retract_coercible_metas : evar_map -> metabinding list * evar_map
+val subst_defined_metas_evars : metabinding list * ('a * existential * constr) list -> constr -> constr option
+
+(** {5 FIXME: Nothing to do here} *)
+
+(*********************************************************
+   Sort/universe variables *)
+
+(** Rigid or flexible universe variables *)
+
+type rigid = 
+  | UnivRigid
+  | UnivFlexible of bool (** Is substitution by an algebraic ok? *)
+
+val univ_rigid : rigid
+val univ_flexible : rigid
+val univ_flexible_alg : rigid
+
+type 'a in_evar_universe_context = 'a * evar_universe_context
+
+val evar_universe_context_set : evar_universe_context -> Univ.universe_context_set
+val evar_universe_context_constraints : evar_universe_context -> Univ.constraints
+val evar_context_universe_context : evar_universe_context -> Univ.universe_context
+val evar_universe_context_of : Univ.universe_context_set -> evar_universe_context
+val empty_evar_universe_context : evar_universe_context
+val union_evar_universe_context : evar_universe_context -> evar_universe_context ->
+  evar_universe_context
+val evar_universe_context_subst : evar_universe_context -> Universes.universe_opt_subst
+
+(** Raises Not_found if not a name for a universe in this map. *)
+val universe_of_name : evar_map -> string -> Univ.universe_level
+val add_universe_name : evar_map -> string -> Univ.universe_level -> evar_map
+
+val universes : evar_map -> Univ.universes
+
+val add_constraints_context : evar_universe_context -> 
+  Univ.constraints -> evar_universe_context
+
+
+val normalize_evar_universe_context_variables : evar_universe_context -> 
+  Univ.universe_subst in_evar_universe_context
+
+val normalize_evar_universe_context : evar_universe_context -> 
+  evar_universe_context
+
+val new_univ_level_variable : ?name:string -> rigid -> evar_map -> evar_map * Univ.universe_level
+val new_univ_variable : ?name:string -> rigid -> evar_map -> evar_map * Univ.universe
+val new_sort_variable : ?name:string -> rigid -> evar_map -> evar_map * sorts
+val make_flexible_variable : evar_map -> bool -> Univ.universe_level -> evar_map
+val is_sort_variable : evar_map -> sorts -> Univ.universe_level option 
+(** [is_sort_variable evm s] returns [Some u] or [None] if [s] is 
+    not a local sort variable declared in [evm] *)
+val is_flexible_level : evar_map -> Univ.Level.t -> bool
+
+val whd_sort_variable : evar_map -> constr -> constr
+(* val normalize_universe_level : evar_map -> Univ.universe_level -> Univ.universe_level *)
+val normalize_universe : evar_map -> Univ.universe -> Univ.universe
+val normalize_universe_instance : evar_map -> Univ.universe_instance -> Univ.universe_instance
+
+val set_leq_sort : env -> evar_map -> sorts -> sorts -> evar_map
+val set_eq_sort : env -> evar_map -> sorts -> sorts -> evar_map
+val has_lub : evar_map -> Univ.universe -> Univ.universe -> evar_map
+val set_eq_level : evar_map -> Univ.universe_level -> Univ.universe_level -> evar_map
+val set_leq_level : evar_map -> Univ.universe_level -> Univ.universe_level -> evar_map
+val set_eq_instances : ?flex:bool -> 
+  evar_map -> Univ.universe_instance -> Univ.universe_instance -> evar_map
+
+val check_eq : evar_map -> Univ.universe -> Univ.universe -> bool
+val check_leq : evar_map -> Univ.universe -> Univ.universe -> bool
+
+val evar_universe_context : evar_map -> evar_universe_context
+val universe_context_set : evar_map -> Univ.universe_context_set
+val universe_context : evar_map -> Univ.universe_context
+val universe_subst : evar_map -> Universes.universe_opt_subst
+val universes : evar_map -> Univ.universes
+
+
+val merge_universe_context : evar_map -> evar_universe_context -> evar_map
+val set_universe_context : evar_map -> evar_universe_context -> evar_map
+
+val merge_context_set : rigid -> evar_map -> Univ.universe_context_set -> evar_map
+val merge_universe_subst : evar_map -> Universes.universe_opt_subst -> evar_map
+
+val with_context_set : rigid -> evar_map -> 'a Univ.in_universe_context_set -> evar_map * 'a
+
+val nf_univ_variables : evar_map -> evar_map * Univ.universe_subst
+val abstract_undefined_variables : evar_universe_context -> evar_universe_context
+
+val refresh_undefined_universes : evar_map -> evar_map * Univ.universe_level_subst
+
+val nf_constraints : evar_map -> evar_map
+
+(** Polymorphic universes *)
+
+val fresh_sort_in_family : ?rigid:rigid -> env -> evar_map -> sorts_family -> evar_map * sorts
+val fresh_constant_instance : env -> evar_map -> constant -> evar_map * pconstant
+val fresh_inductive_instance : env -> evar_map -> inductive -> evar_map * pinductive
+val fresh_constructor_instance : env -> evar_map -> constructor -> evar_map * pconstructor
+
+val fresh_global : ?rigid:rigid -> ?names:Univ.Instance.t -> env -> evar_map -> 
+  Globnames.global_reference -> evar_map * constr
+
+(********************************************************************
+  Conversion w.r.t. an evar map: might generate universe unifications 
+  that are kept in the evarmap.
+  Raises [NotConvertible]. *)
+
+val conversion : env -> evar_map -> conv_pb -> constr -> constr -> evar_map
+
+val test_conversion : env -> evar_map -> conv_pb -> constr -> constr -> bool
+(** This one forgets about the assignemts of universes. *)
+
+val eq_constr_univs : evar_map -> constr -> constr -> evar_map * bool
+(** Syntactic equality up to universes, recording the associated constraints *)
+
+val e_eq_constr_univs : evar_map ref -> constr -> constr -> bool
+(** Syntactic equality up to universes. *)
+
+val eq_constr_univs_test : evar_map -> constr -> constr -> bool
+(** Syntactic equality up to universes, throwing away the (consistent) constraints
+    in case of success. *)
+
+(********************************************************************)
+(* constr with holes and pending resolution of classes, conversion  *)
+(* problems, candidates, etc.                                       *)
+
+type pending = (* before: *) evar_map * (* after: *) evar_map
+
+type pending_constr = pending * constr
+
+type open_constr = evar_map * constr (* Special case when before is empty *)
+
+(** Partially constructed constrs. *)
+
+type unsolvability_explanation = SeveralInstancesFound of int
+(** Failure explanation. *)
+
+val pr_existential_key : evar_map -> evar -> Pp.std_ppcmds
+
+(** {5 Debug pretty-printers} *)
+
+val pr_evar_info : evar_info -> Pp.std_ppcmds
+val pr_evar_constraints : evar_constraint list -> Pp.std_ppcmds
+val pr_evar_map : ?with_univs:bool -> int option -> evar_map -> Pp.std_ppcmds
+val pr_evar_map_filter : ?with_univs:bool -> (Evar.t -> evar_info -> bool) ->
+  evar_map -> Pp.std_ppcmds
+val pr_metaset : Metaset.t -> Pp.std_ppcmds
+val pr_evar_universe_context : evar_universe_context -> Pp.std_ppcmds
+val pr_evd_level : evar_map -> Univ.Level.t -> Pp.std_ppcmds
+
+(** {5 Deprecated functions} *)
+
+val create_evar_defs      : evar_map -> evar_map
+(** Create an [evar_map] with empty meta map: *)
+
+val create_goal_evar_defs : evar_map -> evar_map
diff --git a/engine/logic_monad.ml b/engine/logic_monad.ml
new file mode 100644
index 000000000..d509670ec
--- /dev/null
+++ b/engine/logic_monad.ml
@@ -0,0 +1,326 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(** This file defines the low-level monadic operations used by the
+    tactic monad. The monad is divided into two layers: a non-logical
+    layer which consists in operations which will not (or cannot) be
+    backtracked in case of failure (input/output or persistent state)
+    and a logical layer which handles backtracking, proof
+    manipulation, and any other effect which needs to backtrack. *)
+
+
+(** {6 Exceptions} *)
+
+
+(** To help distinguish between exceptions raised by the IO monad from
+    the one used natively by Coq, the former are wrapped in
+    [Exception].  It is only used internally so that [catch] blocks of
+    the IO monad would only catch exceptions raised by the [raise]
+    function of the IO monad, and not for instance, by system
+    interrupts. Also used in [Proofview] to avoid capturing exception
+    from the IO monad ([Proofview] catches errors in its compatibility
+    layer, and when lifting goal-level expressions). *)
+exception Exception of exn
+(** This exception is used to signal abortion in [timeout] functions. *)
+exception Timeout
+(** This exception is used by the tactics to signal failure by lack of
+    successes, rather than some other exceptions (like system
+    interrupts). *)
+exception TacticFailure of exn
+
+let _ = Errors.register_handler begin function
+  | Timeout -> Errors.errorlabstrm "Some timeout function" (Pp.str"Timeout!")
+  | Exception e -> Errors.print e
+  | TacticFailure e -> Errors.print e
+  | _ -> Pervasives.raise Errors.Unhandled
+end
+
+(** {6 Non-logical layer} *)
+
+(** The non-logical monad is a simple [unit -> 'a] (i/o) monad. The
+    operations are simple wrappers around corresponding usual
+    operations and require little documentation. *)
+module NonLogical =
+struct
+
+  (* The functions in this module follow the pattern that they are
+     defined with the form [(); fun ()->...]. This is an optimisation
+     which signals to the compiler that the function is usually partially
+     applied up to the [();]. Without this annotation, partial
+     applications can be significantly slower.
+
+     Documentation of this behaviour can be found at:
+     https://ocaml.janestreet.com/?q=node/30 *)
+
+  include Monad.Make(struct
+    type 'a t = unit -> 'a
+
+    let return a = (); fun () -> a
+    let (>>=) a k = (); fun () -> k (a ()) ()
+    let (>>) a k = (); fun () -> a (); k ()
+    let map f a = (); fun () -> f (a ())
+  end)
+
+  type 'a ref = 'a Pervasives.ref
+
+  let ignore a = (); fun () -> ignore (a ())
+
+  let ref a = (); fun () -> Pervasives.ref a
+
+  (** [Pervasives.(:=)] *)
+  let (:=) r a = (); fun () -> r := a
+
+  (** [Pervasives.(!)] *)
+  let (!) = fun r -> (); fun () -> ! r
+
+  (** [Pervasives.raise]. Except that exceptions are wrapped with
+      {!Exception}. *)
+  let raise ?info = fun e -> (); fun () -> Exninfo.raise ?info (Exception e)
+
+  (** [try ... with ...] but restricted to {!Exception}. *)
+  let catch = fun s h -> ();
+    fun () -> try s ()
+      with Exception e as src ->
+        let (src, info) = Errors.push src in
+        h (e, info) ()
+
+  let read_line = fun () -> try Pervasives.read_line () with e ->
+    let (e, info) = Errors.push e in raise ~info e ()
+
+  let print_char = fun c -> (); fun () -> print_char c
+
+  (** {!Pp.pp}. The buffer is also flushed. *)
+  let print = fun s -> (); fun () -> try Pp.msg_info s; Pp.pp_flush () with e ->
+    let (e, info) = Errors.push e in raise ~info e ()
+
+  let timeout = fun n t -> (); fun () ->
+    Control.timeout n t (Exception Timeout)
+
+  let make f = (); fun () ->
+    try f ()
+    with e when Errors.noncritical e ->
+      let (e, info) = Errors.push e in
+      Util.iraise (Exception e, info)
+
+  let run = fun x ->
+    try x () with Exception e as src ->
+      let (src, info) = Errors.push src in
+      Util.iraise (e, info)
+end
+
+(** {6 Logical layer} *)
+
+(** The logical monad is a backtracking monad on top of which is
+    layered a state monad (which is used to implement all of read/write,
+    read only, and write only effects). The state monad being layered on
+    top of the backtracking monad makes it so that the state is
+    backtracked on failure.
+
+    Backtracking differs from regular exception in that, writing (+)
+    for exception catching and (>>=) for bind, we require the
+    following extra distributivity laws:
+
+    x+(y+z) = (x+y)+z
+
+    zero+x = x
+
+    x+zero = x
+
+    (x+y)>>=k = (x>>=k)+(y>>=k) *)
+
+(** A view type for the logical monad, which is a form of list, hence
+    we can decompose it with as a list. *)
+type ('a, 'b) list_view =
+  | Nil of Exninfo.iexn
+  | Cons of 'a * 'b
+
+module type Param = sig
+
+  (** Read only *)
+  type e
+
+  (** Write only *)
+  type w
+
+  (** [w] must be a monoid *)
+  val wunit : w
+  val wprod : w -> w -> w
+
+  (** Read-write *)
+  type s
+
+  (** Update-only. Essentially a writer on [u->u]. *)
+  type u
+
+  (** [u] must be pointed. *)
+  val uunit : u
+
+end
+
+
+module Logical (P:Param) =
+struct
+
+  (** All three of environment, writer and state are coded as a single
+      state-passing-style monad.*)
+  type state = {
+    rstate : P.e;
+    ustate : P.u;
+    wstate : P.w;
+    sstate : P.s;
+  }
+
+  (** Double-continuation backtracking monads are reasonable folklore
+      for "search" implementations (including the Tac interactive
+      prover's tactics). Yet it's quite hard to wrap your head around
+      these.  I recommand reading a few times the "Backtracking,
+      Interleaving, and Terminating Monad Transformers" paper by
+      O. Kiselyov, C. Shan, D. Friedman, and A. Sabry.  The peculiar
+      shape of the monadic type is reminiscent of that of the
+      continuation monad transformer.
+
+      The paper also contains the rational for the [split] abstraction.
+
+      An explanation of how to derive such a monad from mathematical
+      principles can be found in "Kan Extensions for Program
+      Optimisation" by Ralf Hinze.
+
+      A somewhat concrete view is that the type ['a iolist] is, in fact
+      the impredicative encoding of the following stream type:
+
+      [type 'a _iolist' = Nil of exn | Cons of 'a*'a iolist'
+      and 'a iolist = 'a _iolist NonLogical.t]
+
+      Using impredicative encoding avoids intermediate allocation and
+      is, empirically, very efficient in Ocaml. It also has the
+      practical benefit that the monadic operation are independent of
+      the underlying monad, which simplifies the code and side-steps
+      the limited inlining of Ocaml.
+
+      In that vision, [bind] is simply [concat_map] (though the cps
+      version is significantly simpler), [plus] is concatenation, and
+      [split] is pattern-matching. *)
+  type rich_exn = Exninfo.iexn
+
+  type 'a iolist =
+      { iolist : 'r. (rich_exn -> 'r NonLogical.t) ->
+                     ('a -> (rich_exn -> 'r NonLogical.t) -> 'r NonLogical.t) ->
+                     'r NonLogical.t }
+
+  include Monad.Make(struct
+    type 'a t = state -> ('a * state) iolist
+
+    let return x : 'a t = (); fun s ->
+      { iolist = fun nil cons -> cons (x, s) nil }
+
+    let (>>=) (m : 'a t) (f : 'a -> 'b t) : 'b t = (); fun s ->
+      let m = m s in
+      { iolist = fun nil cons ->
+        m.iolist nil (fun (x, s) next -> (f x s).iolist next cons) }
+
+    let (>>) (m : unit t) (f : 'a t) : 'a t = (); fun s ->
+      let m = m s in
+      { iolist = fun nil cons ->
+        m.iolist nil (fun ((), s) next -> (f s).iolist next cons) }
+
+    let map (f : 'a -> 'b) (m : 'a t) : 'b t = (); fun s ->
+      let m = m s in
+      { iolist = fun nil cons -> m.iolist nil (fun (x, s) next -> cons (f x, s) next) }
+
+  end)
+
+  let zero e : 'a t = (); fun s ->
+    { iolist = fun nil cons -> nil e }
+
+  let plus m1 m2 : 'a t = (); fun s ->
+    let m1 = m1 s in
+    { iolist = fun nil cons -> m1.iolist (fun e -> (m2 e s).iolist nil cons) cons }
+
+  let ignore (m : 'a t) : unit t = (); fun s ->
+    let m = m s in
+    { iolist = fun nil cons -> m.iolist nil (fun (_, s) next -> cons ((), s) next) }
+
+  let lift (m : 'a NonLogical.t) : 'a t = (); fun s ->
+    { iolist = fun nil cons -> NonLogical.(m >>= fun x -> cons (x, s) nil) }
+
+  (** State related *)
+
+  let get : P.s t = (); fun s ->
+    { iolist = fun nil cons -> cons (s.sstate, s) nil }
+
+  let set (sstate : P.s) : unit t = (); fun s ->
+    { iolist = fun nil cons -> cons ((), { s with sstate }) nil }
+
+  let modify (f : P.s -> P.s) : unit t = (); fun s ->
+    { iolist = fun nil cons -> cons ((), { s with sstate = f s.sstate }) nil }
+
+  let current : P.e t = (); fun s ->
+    { iolist = fun nil cons -> cons (s.rstate, s) nil }
+
+  let local (type a) (e:P.e) (m:a t) : a t = (); fun s ->
+    let m = m { s with rstate = e } in
+    { iolist = fun nil cons ->
+      m.iolist nil (fun (x,s') next -> cons (x,{s' with rstate=s.rstate}) next) }
+
+  let put (w : P.w) : unit t = (); fun s ->
+    { iolist = fun nil cons -> cons ((), { s with wstate = P.wprod s.wstate w }) nil }
+
+  let update (f : P.u -> P.u) : unit t = (); fun s ->
+    { iolist = fun nil cons -> cons ((), { s with ustate = f s.ustate }) nil }
+
+  (** List observation *)
+
+  let once (m : 'a t) : 'a t = (); fun s ->
+    let m = m s in
+    { iolist = fun nil cons -> m.iolist nil (fun x _ -> cons x nil) }
+
+  let break (f : rich_exn -> rich_exn option) (m : 'a t) : 'a t = (); fun s ->
+    let m = m s in
+    { iolist = fun nil cons ->
+      m.iolist nil (fun x next -> cons x (fun e -> match f e with None -> next e | Some e -> nil e))
+    }
+
+  (** For [reflect] and [split] see the "Backtracking, Interleaving,
+      and Terminating Monad Transformers" paper.  *)
+  type 'a reified = ('a, rich_exn -> 'a reified) list_view NonLogical.t
+
+  let rec reflect (m : 'a reified) : 'a iolist =
+    { iolist = fun nil cons ->
+      let next = function
+      | Nil e -> nil e
+      | Cons (x, l) -> cons x (fun e -> (reflect (l e)).iolist nil cons)
+      in
+      NonLogical.(m >>= next)
+    }
+
+  let split (m : 'a t) : ('a, rich_exn -> 'a t) list_view t = (); fun s ->
+    let m = m s in
+    let rnil e = NonLogical.return (Nil e) in
+    let rcons p l = NonLogical.return (Cons (p, l)) in
+    { iolist = fun nil cons ->
+      let open NonLogical in
+      m.iolist rnil rcons >>= begin function
+      | Nil e -> cons (Nil e, s) nil
+      | Cons ((x, s), l) ->
+        let l e = (); fun _ -> reflect (l e) in
+        cons (Cons (x, l), s) nil
+      end }
+
+  let run m r s =
+    let s = { wstate = P.wunit; ustate = P.uunit; rstate = r; sstate = s } in
+    let m = m s in
+    let rnil e = NonLogical.return (Nil e) in
+    let rcons (x, s) l =
+      let p = (x, s.sstate, s.wstate, s.ustate) in
+      NonLogical.return (Cons (p, l))
+    in
+    m.iolist rnil rcons
+
+  let repr x = x
+
+ end
diff --git a/engine/logic_monad.mli b/engine/logic_monad.mli
new file mode 100644
index 000000000..ab729aff7
--- /dev/null
+++ b/engine/logic_monad.mli
@@ -0,0 +1,157 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(** This file defines the low-level monadic operations used by the
+    tactic monad. The monad is divided into two layers: a non-logical
+    layer which consists in operations which will not (or cannot) be
+    backtracked in case of failure (input/output or persistent state)
+    and a logical layer which handles backtracking, proof
+    manipulation, and any other effect which needs to backtrack. *)
+
+
+(** {6 Exceptions} *)
+
+
+(** To help distinguish between exceptions raised by the IO monad from
+    the one used natively by Coq, the former are wrapped in
+    [Exception].  It is only used internally so that [catch] blocks of
+    the IO monad would only catch exceptions raised by the [raise]
+    function of the IO monad, and not for instance, by system
+    interrupts. Also used in [Proofview] to avoid capturing exception
+    from the IO monad ([Proofview] catches errors in its compatibility
+    layer, and when lifting goal-level expressions). *)
+exception Exception of exn
+(** This exception is used to signal abortion in [timeout] functions. *)
+exception Timeout
+(** This exception is used by the tactics to signal failure by lack of
+    successes, rather than some other exceptions (like system
+    interrupts). *)
+exception TacticFailure of exn
+
+
+(** {6 Non-logical layer} *)
+
+(** The non-logical monad is a simple [unit -> 'a] (i/o) monad. The
+    operations are simple wrappers around corresponding usual
+    operations and require little documentation. *)
+module NonLogical : sig
+
+  include Monad.S
+
+  val ignore : 'a t -> unit t
+
+  type 'a ref
+
+  val ref : 'a -> 'a ref t
+  (** [Pervasives.(:=)] *)
+  val (:=) : 'a ref -> 'a -> unit t
+  (** [Pervasives.(!)] *)
+  val (!) : 'a ref -> 'a t
+
+  val read_line : string t
+  val print_char : char -> unit t
+  (** {!Pp.pp}. The buffer is also flushed. *)
+  val print : Pp.std_ppcmds -> unit t
+
+  (** [Pervasives.raise]. Except that exceptions are wrapped with
+      {!Exception}. *)
+  val raise : ?info:Exninfo.info -> exn -> 'a t
+  (** [try ... with ...] but restricted to {!Exception}. *)
+  val catch : 'a t -> (Exninfo.iexn -> 'a t) -> 'a t
+  val timeout : int -> 'a t -> 'a t
+
+  (** Construct a monadified side-effect. Exceptions raised by the argument are
+      wrapped with {!Exception}. *)
+  val make : (unit -> 'a) -> 'a t
+
+  (** [run] performs effects. *)
+  val run : 'a t -> 'a
+
+end
+
+
+(** {6 Logical layer} *)
+
+(** The logical monad is a backtracking monad on top of which is
+    layered a state monad (which is used to implement all of read/write,
+    read only, and write only effects). The state monad being layered on
+    top of the backtracking monad makes it so that the state is
+    backtracked on failure.
+
+    Backtracking differs from regular exception in that, writing (+)
+    for exception catching and (>>=) for bind, we require the
+    following extra distributivity laws:
+
+    x+(y+z) = (x+y)+z
+
+    zero+x = x
+
+    x+zero = x
+
+    (x+y)>>=k = (x>>=k)+(y>>=k) *)
+
+(** A view type for the logical monad, which is a form of list, hence
+    we can decompose it with as a list. *)
+type ('a, 'b) list_view =
+| Nil of Exninfo.iexn
+| Cons of 'a * 'b
+
+(** The monad is parametrised in the types of state, environment and
+    writer. *)
+module type Param = sig
+
+  (** Read only *)
+  type e
+
+  (** Write only *)
+  type w
+
+  (** [w] must be a monoid *)
+  val wunit : w
+  val wprod : w -> w -> w
+
+  (** Read-write *)
+  type s
+
+  (** Update-only. Essentially a writer on [u->u]. *)
+  type u
+
+  (** [u] must be pointed. *)
+  val uunit : u
+
+end
+
+module Logical (P:Param) : sig
+
+  include Monad.S
+
+  val ignore : 'a t -> unit t
+
+  val set : P.s -> unit t
+  val get : P.s t
+  val modify : (P.s -> P.s) -> unit t
+  val put : P.w -> unit t
+  val current : P.e t
+  val local : P.e -> 'a t -> 'a t
+  val update : (P.u -> P.u) -> unit t
+
+  val zero : Exninfo.iexn -> 'a t
+  val plus : 'a t -> (Exninfo.iexn -> 'a t) -> 'a t
+  val split : 'a t -> (('a,(Exninfo.iexn->'a t)) list_view) t
+  val once : 'a t -> 'a t
+  val break : (Exninfo.iexn -> Exninfo.iexn option) -> 'a t -> 'a t
+
+  val lift : 'a NonLogical.t -> 'a t
+
+  type 'a reified
+
+  val repr : 'a reified -> ('a, Exninfo.iexn -> 'a reified) list_view NonLogical.t
+
+  val run : 'a t -> P.e -> P.s -> ('a * P.s * P.w * P.u) reified
+
+end
diff --git a/engine/namegen.ml b/engine/namegen.ml
new file mode 100644
index 000000000..5aca11ae6
--- /dev/null
+++ b/engine/namegen.ml
@@ -0,0 +1,394 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* Created from contents that was formerly in termops.ml and
+   nameops.ml, Nov 2009 *)
+
+(* This file is about generating new or fresh names and dealing with
+   alpha-renaming *)
+
+open Util
+open Names
+open Term
+open Vars
+open Nametab
+open Nameops
+open Libnames
+open Globnames
+open Environ
+open Termops
+
+(**********************************************************************)
+(* Conventional names *)
+
+let default_prop_string = "H"
+let default_prop_ident = Id.of_string default_prop_string
+
+let default_small_string = "H"
+let default_small_ident = Id.of_string default_small_string
+
+let default_type_string = "X"
+let default_type_ident = Id.of_string default_type_string
+
+let default_non_dependent_string = "H"
+let default_non_dependent_ident = Id.of_string default_non_dependent_string
+
+let default_dependent_ident = Id.of_string "x"
+
+(**********************************************************************)
+(* Globality of identifiers *)
+
+let is_imported_modpath = function
+  | MPfile dp ->
+    let rec find_prefix = function
+      |MPfile dp1 -> not (DirPath.equal dp1 dp)
+      |MPdot(mp,_) -> find_prefix mp
+      |MPbound(_) -> false
+    in find_prefix (Lib.current_mp ())
+  | _ -> false
+
+let is_imported_ref = function
+  | VarRef _ -> false
+  | IndRef (kn,_)
+  | ConstructRef ((kn,_),_) ->
+      let (mp,_,_) = repr_mind kn in is_imported_modpath mp
+  | ConstRef kn ->
+      let (mp,_,_) = repr_con kn in is_imported_modpath mp
+
+let is_global id =
+  try
+    let ref = locate (qualid_of_ident id) in
+    not (is_imported_ref ref)
+  with Not_found ->
+    false
+
+let is_constructor id =
+  try
+    match locate (qualid_of_ident id) with
+      | ConstructRef _ -> true
+      | _ -> false
+  with Not_found ->
+    false
+
+(**********************************************************************)
+(* Generating "intuitive" names from its type *)
+
+let head_name c = (* Find the head constant of a constr if any *)
+  let rec hdrec c =
+    match kind_of_term c with
+    | Prod (_,_,c) | Lambda (_,_,c) | LetIn (_,_,_,c)
+    | Cast (c,_,_) | App (c,_) -> hdrec c
+    | Proj (kn,_) -> Some (Label.to_id (con_label (Projection.constant kn)))
+    | Const _ | Ind _ | Construct _ | Var _ ->
+	Some (basename_of_global (global_of_constr c))
+    | Fix ((_,i),(lna,_,_)) | CoFix (i,(lna,_,_)) ->
+	Some (match lna.(i) with Name id -> id | _ -> assert false)
+    | Sort _ | Rel _ | Meta _|Evar _|Case (_, _, _, _) -> None
+  in
+  hdrec c
+
+let lowercase_first_char id = (* First character of a constr *)
+  Unicode.lowercase_first_char (Id.to_string id)
+
+let sort_hdchar = function
+  | Prop(_) -> "P"
+  | Type(_) -> "T"
+
+let hdchar env c =
+  let rec hdrec k c =
+    match kind_of_term c with
+    | Prod (_,_,c) | Lambda (_,_,c) | LetIn (_,_,_,c) -> hdrec (k+1) c
+    | Cast (c,_,_) | App (c,_) -> hdrec k c
+    | Proj (kn,_) -> lowercase_first_char (Label.to_id (con_label (Projection.constant kn)))
+    | Const (kn,_) -> lowercase_first_char (Label.to_id (con_label kn))
+    | Ind (x,_) -> lowercase_first_char (basename_of_global (IndRef x))
+    | Construct (x,_) -> lowercase_first_char (basename_of_global (ConstructRef x))
+    | Var id  -> lowercase_first_char id
+    | Sort s -> sort_hdchar s
+    | Rel n ->
+	(if n<=k then "p" (* the initial term is flexible product/function *)
+	 else
+	   try match Environ.lookup_rel (n-k) env with
+	     | (Name id,_,_)   -> lowercase_first_char id
+	     | (Anonymous,_,t) -> hdrec 0 (lift (n-k) t)
+	   with Not_found -> "y")
+    | Fix ((_,i),(lna,_,_)) | CoFix (i,(lna,_,_)) ->
+	let id = match lna.(i) with Name id -> id | _ -> assert false in
+	lowercase_first_char id
+    | Evar _ (* We could do better... *)
+    | Meta _ | Case (_, _, _, _) -> "y"
+  in
+  hdrec 0 c
+
+let id_of_name_using_hdchar env a = function
+  | Anonymous -> Id.of_string (hdchar env a)
+  | Name id   -> id
+
+let named_hd env a = function
+  | Anonymous -> Name (Id.of_string (hdchar env a))
+  | x         -> x
+
+let mkProd_name   env (n,a,b) = mkProd (named_hd env a n, a, b)
+let mkLambda_name env (n,a,b) = mkLambda (named_hd env a n, a, b)
+
+let lambda_name = mkLambda_name
+let prod_name = mkProd_name
+
+let prod_create   env (a,b) = mkProd (named_hd env a Anonymous, a, b)
+let lambda_create env (a,b) =  mkLambda (named_hd env a Anonymous, a, b)
+
+let name_assumption env (na,c,t) =
+  match c with
+    | None      -> (named_hd env t na, None, t)
+    | Some body -> (named_hd env body na, c, t)
+
+let name_context env hyps =
+  snd
+    (List.fold_left
+       (fun (env,hyps) d ->
+	  let d' = name_assumption env d in (push_rel d' env, d' :: hyps))
+       (env,[]) (List.rev hyps))
+
+let mkProd_or_LetIn_name env b d = mkProd_or_LetIn (name_assumption env d) b
+let mkLambda_or_LetIn_name env b d = mkLambda_or_LetIn (name_assumption env d)b
+
+let it_mkProd_or_LetIn_name env b hyps =
+  it_mkProd_or_LetIn b (name_context env hyps)
+let it_mkLambda_or_LetIn_name env b hyps =
+  it_mkLambda_or_LetIn b (name_context env hyps)
+
+(**********************************************************************)
+(* Fresh names *)
+
+(* Looks for next "good" name by lifting subscript *)
+
+let next_ident_away_from id bad =
+  let rec name_rec id = if bad id then name_rec (lift_subscript id) else id in
+  name_rec id
+
+(* Restart subscript from x0 if name starts with xN, or x00 if name
+   starts with x0N, etc *)
+
+let restart_subscript id =
+  if not (has_subscript id) then id else
+    (* It would probably be better with something in the spirit of
+     *** make_ident id (Some 0) *** but compatibility would be lost... *)
+    forget_subscript id
+
+let rec to_avoid id = function
+| [] -> false
+| id' :: avoid -> Id.equal id id' || to_avoid id avoid
+
+let occur_rel p env id =
+  try
+    let name = lookup_name_of_rel p env in
+    begin match name with
+    | Name id' -> Id.equal id' id
+    | Anonymous -> false
+    end
+  with Not_found -> false (* Unbound indice : may happen in debug *)
+
+let visibly_occur_id id (nenv,c) =
+  let rec occur n c = match kind_of_term c with
+    | Const _ | Ind _ | Construct _ | Var _
+      when
+        let short = shortest_qualid_of_global Id.Set.empty (global_of_constr c) in
+        qualid_eq short (qualid_of_ident id) ->
+      raise Occur
+    | Rel p when p>n && occur_rel (p-n) nenv id -> raise Occur
+    | _ -> iter_constr_with_binders succ occur n c
+  in
+  try occur 1 c; false
+  with Occur -> true
+    | Not_found -> false (* Happens when a global is not in the env *)
+
+(* Now, there are different renaming strategies... *)
+
+(* 1- Looks for a fresh name for printing in cases pattern *)
+
+let next_name_away_in_cases_pattern env_t na avoid =
+  let id = match na with Name id -> id | Anonymous -> default_dependent_ident in
+  let bad id = to_avoid id avoid || is_constructor id
+                                 || visibly_occur_id id env_t in
+  next_ident_away_from id bad
+
+(* 2- Looks for a fresh name for introduction in goal *)
+
+(* The legacy strategy for renaming introduction variables is not very uniform:
+   - if the name to use is fresh in the context but used as a global
+     name, then a fresh name is taken by finding a free subscript
+     starting from the current subscript;
+   - but if the name to use is not fresh in the current context, the fresh
+     name is taken by finding a free subscript starting from 0 *)
+
+let next_ident_away_in_goal id avoid =
+  let id = if to_avoid id avoid then restart_subscript id else id in
+  let bad id = to_avoid id avoid || (is_global id && not (is_section_variable id)) in
+  next_ident_away_from id bad
+
+let next_name_away_in_goal na avoid =
+  let id = match na with
+    | Name id -> id
+    | Anonymous -> default_non_dependent_ident in
+  next_ident_away_in_goal id avoid
+
+(* 3- Looks for next fresh name outside a list that is moreover valid
+   as a global identifier; the legacy algorithm is that if the name is
+   already used in the list, one looks for a name of same base with
+   lower available subscript; if the name is not in the list but is
+   used globally, one looks for a name of same base with lower subscript
+   beyond the current subscript *)
+
+let next_global_ident_away id avoid =
+  let id = if to_avoid id avoid then restart_subscript id else id in
+  let bad id = to_avoid id avoid || is_global id in
+  next_ident_away_from id bad
+
+(* 4- Looks for next fresh name outside a list; if name already used,
+   looks for same name with lower available subscript *)
+
+let next_ident_away id avoid =
+  if to_avoid id avoid then
+    next_ident_away_from (restart_subscript id) (fun id -> to_avoid id avoid)
+  else id
+
+let next_name_away_with_default default na avoid =
+  let id = match na with Name id -> id | Anonymous -> Id.of_string default in
+  next_ident_away id avoid
+
+let reserved_type_name = ref (fun t -> Anonymous)
+let set_reserved_typed_name f = reserved_type_name := f
+
+let next_name_away_with_default_using_types default na avoid t =
+  let id = match na with
+    | Name id -> id
+    | Anonymous -> match !reserved_type_name t with
+	| Name id -> id
+	| Anonymous -> Id.of_string default in
+  next_ident_away id avoid
+
+let next_name_away = next_name_away_with_default default_non_dependent_string
+
+let make_all_name_different env =
+  let avoid = ref (ids_of_named_context (named_context env)) in
+  process_rel_context
+    (fun (na,c,t) newenv ->
+       let id = next_name_away na !avoid in
+       avoid := id::!avoid;
+       push_rel (Name id,c,t) newenv)
+    env
+
+(* 5- Looks for next fresh name outside a list; avoids also to use names that
+   would clash with short name of global references; if name is already used,
+   looks for name of same base with lower available subscript beyond current
+   subscript *)
+
+let next_ident_away_for_default_printing env_t id avoid =
+  let bad id = to_avoid id avoid || visibly_occur_id id env_t in
+  next_ident_away_from id bad
+
+let next_name_away_for_default_printing env_t na avoid =
+  let id = match na with
+  | Name id   -> id
+  | Anonymous ->
+      (* In principle, an anonymous name is not dependent and will not be *)
+      (* taken into account by the function compute_displayed_name_in; *)
+      (* just in case, invent a valid name *)
+      default_non_dependent_ident in
+  next_ident_away_for_default_printing env_t id avoid
+
+(**********************************************************************)
+(* Displaying terms avoiding bound variables clashes *)
+
+(* Renaming strategy introduced in December 1998:
+
+   - Rule number 1: all names, even if unbound and not displayed, contribute
+     to the list of names to avoid
+   - Rule number 2: only the dependency status is used for deciding if
+     a name is displayed or not
+
+   Example:
+   bool_ind: "forall (P:bool->Prop)(f:(P true))(f:(P false))(b:bool), P b" is
+   displayed "forall P:bool->Prop, P true -> P false -> forall b:bool, P b"
+   but f and f0 contribute to the list of variables to avoid (knowing
+   that f and f0 are how the f's would be named if introduced, assuming
+   no other f and f0 are already used).
+*)
+
+type renaming_flags =
+  | RenamingForCasesPattern of (Name.t list * constr)
+  | RenamingForGoal
+  | RenamingElsewhereFor of (Name.t list * constr)
+
+let next_name_for_display flags =
+  match flags with
+  | RenamingForCasesPattern env_t -> next_name_away_in_cases_pattern env_t
+  | RenamingForGoal -> next_name_away_in_goal
+  | RenamingElsewhereFor env_t -> next_name_away_for_default_printing env_t
+
+(* Remark: Anonymous var may be dependent in Evar's contexts *)
+let compute_displayed_name_in flags avoid na c =
+  match na with
+  | Anonymous when noccurn 1 c ->
+    (Anonymous,avoid)
+  | _ ->
+    let fresh_id = next_name_for_display flags na avoid in
+    let idopt = if noccurn 1 c then Anonymous else Name fresh_id in
+    (idopt, fresh_id::avoid)
+
+let compute_and_force_displayed_name_in flags avoid na c =
+  match na with
+  | Anonymous when noccurn 1 c ->
+    (Anonymous,avoid)
+  | _ ->
+    let fresh_id = next_name_for_display flags na avoid in
+    (Name fresh_id, fresh_id::avoid)
+
+let compute_displayed_let_name_in flags avoid na c =
+  let fresh_id = next_name_for_display flags na avoid in
+  (Name fresh_id, fresh_id::avoid)
+
+let rename_bound_vars_as_displayed avoid env c =
+  let rec rename avoid env c =
+    match kind_of_term c with
+    | Prod (na,c1,c2)  ->
+	let na',avoid' =
+          compute_displayed_name_in
+            (RenamingElsewhereFor (env,c2)) avoid na c2 in
+	mkProd (na', c1, rename avoid' (add_name na' env) c2)
+    | LetIn (na,c1,t,c2) ->
+	let na',avoid' =
+          compute_displayed_let_name_in
+            (RenamingElsewhereFor (env,c2)) avoid na c2 in
+	mkLetIn (na',c1,t, rename avoid' (add_name na' env) c2)
+    | Cast (c,k,t) -> mkCast (rename avoid env c, k,t)
+    | _ -> c
+  in
+  rename avoid env c
+
+(**********************************************************************)
+(* "H"-based naming strategy introduced June 2014 for hypotheses in
+   Prop produced by case/elim/destruct/induction, in place of the
+   strategy that was using the first letter of the type, leading to
+   inelegant "n:~A", "e:t=u", etc. when eliminating sumbool or similar
+   types *)
+
+let h_based_elimination_names = ref false
+
+let use_h_based_elimination_names () =
+  !h_based_elimination_names && Flags.version_strictly_greater Flags.V8_4
+
+open Goptions
+
+let _ = declare_bool_option
+	  { optsync  = true;
+            optdepr  = false;
+	    optname  = "use of \"H\"-based proposition names in elimination tactics";
+	    optkey   = ["Standard";"Proposition";"Elimination";"Names"];
+	    optread  = (fun () -> !h_based_elimination_names);
+	    optwrite = (:=) h_based_elimination_names }
diff --git a/engine/namegen.mli b/engine/namegen.mli
new file mode 100644
index 000000000..f66bc6d88
--- /dev/null
+++ b/engine/namegen.mli
@@ -0,0 +1,102 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Term
+open Context
+open Environ
+
+(*********************************************************************
+   Conventional default names *)
+
+val default_prop_ident : Id.t          (* "H" *)
+val default_small_ident : Id.t         (* "H" *)
+val default_type_ident : Id.t          (* "X" *)
+val default_non_dependent_ident : Id.t (* "H" *)
+val default_dependent_ident : Id.t     (* "x" *)
+
+(*********************************************************************
+   Generating "intuitive" names from their type *)
+
+val lowercase_first_char : Id.t -> string
+val sort_hdchar : sorts -> string
+val hdchar : env -> types -> string
+val id_of_name_using_hdchar : env -> types -> Name.t -> Id.t
+val named_hd : env -> types -> Name.t -> Name.t
+val head_name : types -> Id.t option
+
+val mkProd_name : env -> Name.t * types * types -> types
+val mkLambda_name : env -> Name.t * types * constr -> constr
+
+(** Deprecated synonyms of [mkProd_name] and [mkLambda_name] *)
+val prod_name : env -> Name.t * types * types -> types
+val lambda_name : env -> Name.t * types * constr -> constr
+
+val prod_create : env -> types * types -> constr
+val lambda_create : env -> types * constr -> constr
+val name_assumption : env -> rel_declaration -> rel_declaration
+val name_context : env -> rel_context -> rel_context
+
+val mkProd_or_LetIn_name : env -> types -> rel_declaration -> types
+val mkLambda_or_LetIn_name : env -> constr -> rel_declaration -> constr
+val it_mkProd_or_LetIn_name   : env -> types -> rel_context -> types
+val it_mkLambda_or_LetIn_name : env -> constr -> rel_context -> constr
+
+(*********************************************************************
+   Fresh names *)
+
+(** Avoid clashing with a name satisfying some predicate *)
+val next_ident_away_from : Id.t -> (Id.t -> bool) -> Id.t
+
+(** Avoid clashing with a name of the given list *)
+val next_ident_away : Id.t -> Id.t list -> Id.t
+
+(** Avoid clashing with a name already used in current module *)
+val next_ident_away_in_goal : Id.t -> Id.t list -> Id.t
+
+(** Avoid clashing with a name already used in current module 
+   but tolerate overwriting section variables, as in goals *)
+val next_global_ident_away : Id.t -> Id.t list -> Id.t
+
+(** Avoid clashing with a constructor name already used in current module *)
+val next_name_away_in_cases_pattern : (Termops.names_context * constr) -> Name.t -> Id.t list -> Id.t
+
+(** Default is [default_non_dependent_ident] *)
+val next_name_away  : Name.t -> Id.t list -> Id.t
+
+val next_name_away_with_default : string -> Name.t -> Id.t list ->
+  Id.t
+
+val next_name_away_with_default_using_types : string -> Name.t ->
+  Id.t list -> types -> Id.t
+
+val set_reserved_typed_name : (types -> Name.t) -> unit
+
+(*********************************************************************
+   Making name distinct for displaying *)
+
+type renaming_flags =
+  | RenamingForCasesPattern of (Name.t list * constr) (** avoid only global constructors *)
+  | RenamingForGoal (** avoid all globals (as in intro) *)
+  | RenamingElsewhereFor of (Name.t list * constr)
+
+val make_all_name_different : env -> env
+
+val compute_displayed_name_in :
+  renaming_flags -> Id.t list -> Name.t -> constr -> Name.t * Id.t list
+val compute_and_force_displayed_name_in :
+  renaming_flags -> Id.t list -> Name.t -> constr -> Name.t * Id.t list
+val compute_displayed_let_name_in :
+  renaming_flags -> Id.t list -> Name.t -> constr -> Name.t * Id.t list
+val rename_bound_vars_as_displayed :
+  Id.t list -> Name.t list -> types -> types
+
+(**********************************************************************)
+(* Naming strategy for arguments in Prop when eliminating inductive types *)
+
+val use_h_based_elimination_names : unit -> bool
diff --git a/engine/termops.ml b/engine/termops.ml
new file mode 100644
index 000000000..9f04faa83
--- /dev/null
+++ b/engine/termops.ml
@@ -0,0 +1,1023 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \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 Context
+open Environ
+
+(* Sorts and sort family *)
+
+let print_sort = function
+  | Prop Pos -> (str "Set")
+  | Prop Null -> (str "Prop")
+  | Type u -> (str "Type(" ++ Univ.Universe.pr u ++ str ")")
+
+let pr_sort_family = function
+  | InSet -> (str "Set")
+  | InProp -> (str "Prop")
+  | InType -> (str "Type")
+
+let pr_name = function
+  | Name id -> pr_id id
+  | Anonymous -> str "_"
+
+let pr_con sp = str(string_of_con sp)
+
+let pr_fix pr_constr ((t,i),(lna,tl,bl)) =
+  let fixl = Array.mapi (fun i na -> (na,t.(i),tl.(i),bl.(i))) lna in
+  hov 1
+      (str"fix " ++ int i ++ spc() ++  str"{" ++
+         v 0 (prlist_with_sep spc (fun (na,i,ty,bd) ->
+           pr_name na ++ str"/" ++ int i ++ str":" ++ pr_constr ty ++
+	   cut() ++ str":=" ++ pr_constr bd) (Array.to_list fixl)) ++
+         str"}")
+
+let pr_puniverses p u = 
+  if Univ.Instance.is_empty u then p 
+  else p ++ str"(*" ++ Univ.Instance.pr Universes.pr_with_global_universes u ++ str"*)"
+
+let rec pr_constr c = match kind_of_term c with
+  | Rel n -> str "#"++int n
+  | Meta n -> str "Meta(" ++ int n ++ str ")"
+  | Var id -> pr_id id
+  | Sort s -> print_sort s
+  | Cast (c,_, t) -> hov 1
+      (str"(" ++ pr_constr c ++ cut() ++
+       str":" ++ pr_constr t ++ str")")
+  | Prod (Name(id),t,c) -> hov 1
+      (str"forall " ++ pr_id id ++ str":" ++ pr_constr t ++ str"," ++
+       spc() ++ pr_constr c)
+  | Prod (Anonymous,t,c) -> hov 0
+      (str"(" ++ pr_constr t ++ str " ->" ++ spc() ++
+       pr_constr c ++ str")")
+  | Lambda (na,t,c) -> hov 1
+      (str"fun " ++ pr_name na ++ str":" ++
+       pr_constr t ++ str" =>" ++ spc() ++ pr_constr c)
+  | LetIn (na,b,t,c) -> hov 0
+      (str"let " ++ pr_name na ++ str":=" ++ pr_constr b ++
+       str":" ++ brk(1,2) ++ pr_constr t ++ cut() ++
+       pr_constr c)
+  | App (c,l) ->  hov 1
+      (str"(" ++ pr_constr c ++ spc() ++
+       prlist_with_sep spc pr_constr (Array.to_list l) ++ str")")
+  | Evar (e,l) -> hov 1
+      (str"Evar#" ++ int (Evar.repr e) ++ str"{" ++
+       prlist_with_sep spc pr_constr (Array.to_list l) ++str"}")
+  | Const (c,u) -> str"Cst(" ++ pr_puniverses (pr_con c) u ++ str")"
+  | Ind ((sp,i),u) -> str"Ind(" ++ pr_puniverses (pr_mind sp ++ str"," ++ int i) u ++ str")"
+  | Construct (((sp,i),j),u) ->
+      str"Constr(" ++ pr_puniverses (pr_mind sp ++ str"," ++ int i ++ str"," ++ int j) u ++ str")"
+  | Proj (p,c) -> str"Proj(" ++ pr_con (Projection.constant p) ++ str"," ++ bool (Projection.unfolded p) ++ pr_constr c ++ str")"
+  | Case (ci,p,c,bl) -> v 0
+      (hv 0 (str"<"++pr_constr p++str">"++ cut() ++ str"Case " ++
+             pr_constr c ++ str"of") ++ cut() ++
+       prlist_with_sep (fun _ -> brk(1,2)) pr_constr (Array.to_list bl) ++
+      cut() ++ str"end")
+  | Fix f -> pr_fix pr_constr f
+  | CoFix(i,(lna,tl,bl)) ->
+      let fixl = Array.mapi (fun i na -> (na,tl.(i),bl.(i))) lna in
+      hov 1
+        (str"cofix " ++ int i ++ spc() ++  str"{" ++
+         v 0 (prlist_with_sep spc (fun (na,ty,bd) ->
+           pr_name na ++ str":" ++ pr_constr ty ++
+           cut() ++ str":=" ++ pr_constr bd) (Array.to_list fixl)) ++
+         str"}")
+
+let term_printer = ref (fun _ -> pr_constr)
+let print_constr_env t = !term_printer t
+let print_constr t = !term_printer (Global.env()) t
+let set_print_constr f = term_printer := f
+
+let pr_var_decl env (id,c,typ) =
+  let pbody = match c with
+    | None ->  (mt ())
+    | Some c ->
+	(* Force evaluation *)
+	let pb = print_constr_env env c in
+	  (str" := " ++ pb ++ cut () ) in
+  let pt = print_constr_env env typ in
+  let ptyp = (str" : " ++ pt) in
+    (pr_id id ++ hov 0 (pbody ++ ptyp))
+
+let pr_rel_decl env (na,c,typ) =
+  let pbody = match c with
+    | None -> mt ()
+    | Some c ->
+	(* Force evaluation *)
+	let pb = print_constr_env env c in
+	  (str":=" ++ spc () ++ pb ++ spc ()) in
+  let ptyp = print_constr_env env typ in
+    match na with
+      | Anonymous -> hov 0 (str"<>" ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)
+      | Name id -> hov 0 (pr_id id ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)
+
+let print_named_context env =
+  hv 0 (fold_named_context
+	  (fun env d pps ->
+	    pps ++ ws 2 ++ pr_var_decl env d)
+          env ~init:(mt ()))
+
+let print_rel_context env =
+  hv 0 (fold_rel_context
+	  (fun env d pps -> pps ++ ws 2 ++ pr_rel_decl env d)
+          env ~init:(mt ()))
+
+let print_env env =
+  let sign_env =
+    fold_named_context
+      (fun env d pps ->
+         let pidt =  pr_var_decl env d in
+	 (pps ++ fnl () ++ pidt))
+      env ~init:(mt ())
+  in
+  let db_env =
+    fold_rel_context
+      (fun env d pps ->
+         let pnat = pr_rel_decl env d in (pps ++ fnl () ++ pnat))
+      env ~init:(mt ())
+  in
+    (sign_env ++ db_env)
+
+(* [Rel (n+m);...;Rel(n+1)] *)
+let rel_vect n m = Array.init m (fun i -> mkRel(n+m-i))
+
+let rel_list n m =
+  let rec reln l p =
+    if p>m then l else reln (mkRel(n+p)::l) (p+1)
+  in
+  reln [] 1
+
+(* Same as [rel_list] but takes a context as argument and skips let-ins *)
+let extended_rel_list n hyps =
+  let rec reln l p = function
+    | (_,None,_) :: hyps -> reln (mkRel (n+p) :: l) (p+1) hyps
+    | (_,Some _,_) :: hyps -> reln l (p+1) hyps
+    | [] -> l
+  in
+  reln [] 1 hyps
+
+let extended_rel_vect n hyps = Array.of_list (extended_rel_list n hyps)
+
+
+
+let push_rel_assum (x,t) env = push_rel (x,None,t) env
+
+let push_rels_assum assums =
+  push_rel_context (List.map (fun (x,t) -> (x,None,t)) assums)
+
+let push_named_rec_types (lna,typarray,_) env =
+  let ctxt =
+    Array.map2_i
+      (fun i na t ->
+	 match na with
+	   | Name id -> (id, None, lift i t)
+	   | Anonymous -> anomaly (Pp.str "Fix declarations must be named"))
+      lna typarray in
+  Array.fold_left
+    (fun e assum -> push_named assum e) env ctxt
+
+let lookup_rel_id id sign =
+  let rec lookrec n = function
+    | []                     -> raise Not_found
+    | (Anonymous, _, _) :: l -> lookrec (n + 1) l
+    | (Name id', b, t) :: l  ->
+      if Names.Id.equal id' id then (n, b, t) else lookrec (n + 1) l
+  in
+  lookrec 1 sign
+
+(* Constructs either [forall x:t, c] or [let x:=b:t in c] *)
+let mkProd_or_LetIn (na,body,t) c =
+  match body with
+    | None -> mkProd (na, t, c)
+    | Some b -> mkLetIn (na, b, t, c)
+
+(* Constructs either [forall x:t, c] or [c] in which [x] is replaced by [b] *)
+let mkProd_wo_LetIn (na,body,t) c =
+  match body with
+    | None -> mkProd (na,  t, c)
+    | Some b -> subst1 b c
+
+let it_mkProd init = List.fold_left (fun c (n,t)  -> mkProd (n, t, c)) init
+let it_mkLambda init = List.fold_left (fun c (n,t)  -> mkLambda (n, t, c)) init
+
+let it_named_context_quantifier f ~init =
+  List.fold_left (fun c d -> f d c) init
+
+let it_mkProd_or_LetIn init = it_named_context_quantifier mkProd_or_LetIn ~init
+let it_mkProd_wo_LetIn init = it_named_context_quantifier mkProd_wo_LetIn ~init
+let it_mkLambda_or_LetIn init = it_named_context_quantifier mkLambda_or_LetIn ~init
+let it_mkNamedProd_or_LetIn init = it_named_context_quantifier mkNamedProd_or_LetIn ~init
+let it_mkNamedProd_wo_LetIn init = it_named_context_quantifier mkNamedProd_wo_LetIn ~init
+let it_mkNamedLambda_or_LetIn init = it_named_context_quantifier mkNamedLambda_or_LetIn ~init
+
+let it_mkLambda_or_LetIn_from_no_LetIn c decls =
+  let rec aux k decls c = match decls with
+  | [] -> c
+  | (na,Some b,t)::decls -> mkLetIn (na,b,t,aux (k-1) decls (liftn 1 k c))
+  | (na,None,t)::decls -> mkLambda (na,t,aux (k-1) decls c)
+  in aux (List.length decls) (List.rev decls) c
+
+(* *)
+
+(* strips head casts and flattens head applications *)
+let rec strip_head_cast c = match kind_of_term c with
+  | App (f,cl) ->
+      let rec collapse_rec f cl2 = match kind_of_term f with
+	| App (g,cl1) -> collapse_rec g (Array.append cl1 cl2)
+	| Cast (c,_,_) -> collapse_rec c cl2
+	| _ -> if Int.equal (Array.length cl2) 0 then f else mkApp (f,cl2)
+      in
+      collapse_rec f cl
+  | Cast (c,_,_) -> strip_head_cast c
+  | _ -> c
+
+let rec drop_extra_implicit_args c = match kind_of_term c with
+  (* Removed trailing extra implicit arguments, what improves compatibility
+     for constants with recently added maximal implicit arguments *)
+  | App (f,args) when isEvar (Array.last args) ->
+      drop_extra_implicit_args
+	(mkApp (f,fst (Array.chop (Array.length args - 1) args)))
+  | _ -> c
+
+(* Get the last arg of an application *)
+let last_arg c = match kind_of_term c with
+  | App (f,cl) -> Array.last cl
+  | _ -> anomaly (Pp.str "last_arg")
+
+(* Get the last arg of an application *)
+let decompose_app_vect c =
+  match kind_of_term c with
+  | App (f,cl) -> (f, cl)
+  | _ -> (c,[||])
+
+let adjust_app_list_size f1 l1 f2 l2 =
+  let len1 = List.length l1 and len2 = List.length l2 in
+  if Int.equal len1 len2 then (f1,l1,f2,l2)
+  else if len1 < len2 then
+   let extras,restl2 = List.chop (len2-len1) l2 in
+    (f1, l1, applist (f2,extras), restl2)
+  else
+    let extras,restl1 = List.chop (len1-len2) l1 in
+    (applist (f1,extras), restl1, f2, l2)
+
+let adjust_app_array_size f1 l1 f2 l2 =
+  let len1 = Array.length l1 and len2 = Array.length l2 in
+  if Int.equal len1 len2 then (f1,l1,f2,l2)
+  else if len1 < len2 then
+    let extras,restl2 = Array.chop (len2-len1) l2 in
+    (f1, l1, appvect (f2,extras), restl2)
+  else
+    let extras,restl1 = Array.chop (len1-len2) l1 in
+    (appvect (f1,extras), restl1, f2, l2)
+
+(* [map_constr_with_named_binders g f l c] maps [f l] on the immediate
+   subterms of [c]; it carries an extra data [l] (typically a name
+   list) which is processed by [g na] (which typically cons [na] to
+   [l]) at each binder traversal (with name [na]); it is not recursive
+   and the order with which subterms are processed is not specified *)
+
+let map_constr_with_named_binders g f l c = match kind_of_term c with
+  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
+    | Construct _) -> c
+  | Cast (c,k,t) -> mkCast (f l c, k, f l t)
+  | Prod (na,t,c) -> mkProd (na, f l t, f (g na l) c)
+  | Lambda (na,t,c) -> mkLambda (na, f l t, f (g na l) c)
+  | LetIn (na,b,t,c) -> mkLetIn (na, f l b, f l t, f (g na l) c)
+  | App (c,al) -> mkApp (f l c, Array.map (f l) al)
+  | Proj (p,c) -> mkProj (p, f l c)
+  | Evar (e,al) -> mkEvar (e, Array.map (f l) al)
+  | Case (ci,p,c,bl) -> mkCase (ci, f l p, f l c, Array.map (f l) bl)
+  | Fix (ln,(lna,tl,bl)) ->
+      let l' = Array.fold_left (fun l na -> g na l) l lna in
+      mkFix (ln,(lna,Array.map (f l) tl,Array.map (f l') bl))
+  | CoFix(ln,(lna,tl,bl)) ->
+      let l' = Array.fold_left (fun l na -> g na l) l lna in
+      mkCoFix (ln,(lna,Array.map (f l) tl,Array.map (f l') bl))
+
+(* [map_constr_with_binders_left_to_right g f n c] maps [f n] on the
+   immediate subterms of [c]; it carries an extra data [n] (typically
+   a lift index) which is processed by [g] (which typically add 1 to
+   [n]) at each binder traversal; the subterms are processed from left
+   to right according to the usual representation of the constructions
+   (this may matter if [f] does a side-effect); it is not recursive;
+   in fact, the usual representation of the constructions is at the
+   time being almost those of the ML representation (except for
+   (co-)fixpoint) *)
+
+let fold_rec_types g (lna,typarray,_) e =
+  let ctxt = Array.map2_i (fun i na t -> (na, None, lift i t)) lna typarray in
+  Array.fold_left (fun e assum -> g assum e) e ctxt
+
+let map_left2 f a g b =
+  let l = Array.length a in
+  if Int.equal l 0 then [||], [||] else begin
+    let r = Array.make l (f a.(0)) in
+    let s = Array.make l (g b.(0)) in
+    for i = 1 to l - 1 do
+      r.(i) <- f a.(i);
+      s.(i) <- g b.(i)
+    done;
+    r, s
+  end
+
+let map_constr_with_binders_left_to_right g f l c = match kind_of_term c with
+  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
+    | Construct _) -> c
+  | Cast (b,k,t) -> 
+    let b' = f l b in 
+    let t' = f l t in
+      if b' == b && t' == t then c
+      else mkCast (b',k,t')
+  | Prod (na,t,b) ->
+      let t' = f l t in
+      let b' = f (g (na,None,t) l) b in
+	if t' == t && b' == b then c
+	else mkProd (na, t', b')
+  | Lambda (na,t,b) ->
+      let t' = f l t in
+      let b' = f (g (na,None,t) l) b in
+	if t' == t && b' == b then c
+	else mkLambda (na, t', b')
+  | LetIn (na,bo,t,b) ->
+      let bo' = f l bo in
+      let t' = f l t in
+      let b' = f (g (na,Some bo,t) l) b in
+	if bo' == bo && t' == t && b' == b then c
+	else mkLetIn (na, bo', t', b')	    
+  | App (c,[||]) -> assert false
+  | App (t,al) ->
+      (*Special treatment to be able to recognize partially applied subterms*)
+      let a = al.(Array.length al - 1) in
+      let app = (mkApp (t, Array.sub al 0 (Array.length al - 1))) in
+      let app' = f l app in
+      let a' = f l a in
+	if app' == app && a' == a then c
+	else mkApp (app', [| a' |])
+  | Proj (p,b) ->
+    let b' = f l b in
+      if b' == b then c
+      else mkProj (p, b')
+  | Evar (e,al) -> 
+    let al' = Array.map_left (f l) al in
+      if Array.for_all2 (==) al' al then c
+      else mkEvar (e, al')
+  | Case (ci,p,b,bl) ->
+      (* In v8 concrete syntax, predicate is after the term to match! *)
+      let b' = f l b in
+      let p' = f l p in
+      let bl' = Array.map_left (f l) bl in
+	if b' == b && p' == p && bl' == bl then c
+	else mkCase (ci, p', b', bl')
+  | Fix (ln,(lna,tl,bl as fx)) ->
+      let l' = fold_rec_types g fx l in
+      let (tl', bl') = map_left2 (f l) tl (f l') bl in
+	if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
+	then c
+	else mkFix (ln,(lna,tl',bl'))
+  | CoFix(ln,(lna,tl,bl as fx)) ->
+      let l' = fold_rec_types g fx l in
+      let (tl', bl') = map_left2 (f l) tl (f l') bl in
+	if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
+	then c
+	else mkCoFix (ln,(lna,tl',bl'))
+
+(* strong *)
+let map_constr_with_full_binders g f l cstr = match kind_of_term cstr with
+  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
+    | Construct _) -> cstr
+  | Cast (c,k, t) ->
+      let c' = f l c in
+      let t' = f l t in
+      if c==c' && t==t' then cstr else mkCast (c', k, t')
+  | Prod (na,t,c) ->
+      let t' = f l t in
+      let c' = f (g (na,None,t) l) c in
+      if t==t' && c==c' then cstr else mkProd (na, t', c')
+  | Lambda (na,t,c) ->
+      let t' = f l t in
+      let c' = f (g (na,None,t) l) c in
+      if t==t' && c==c' then cstr else  mkLambda (na, t', c')
+  | LetIn (na,b,t,c) ->
+      let b' = f l b in
+      let t' = f l t in
+      let c' = f (g (na,Some b,t) l) c in
+      if b==b' && t==t' && c==c' then cstr else mkLetIn (na, b', t', c')
+  | App (c,al) ->
+      let c' = f l c in
+      let al' = Array.map (f l) al in
+      if c==c' && Array.for_all2 (==) al al' then cstr else mkApp (c', al')
+  | Proj (p,c) -> 
+      let c' = f l c in
+	if c' == c then cstr else mkProj (p, c')
+  | Evar (e,al) ->
+      let al' = Array.map (f l) al in
+      if Array.for_all2 (==) al al' then cstr else mkEvar (e, al')
+  | Case (ci,p,c,bl) ->
+      let p' = f l p in
+      let c' = f l c in
+      let bl' = Array.map (f l) bl in
+      if p==p' && c==c' && Array.for_all2 (==) bl bl' then cstr else
+        mkCase (ci, p', c', bl')
+  | Fix (ln,(lna,tl,bl)) ->
+      let tl' = Array.map (f l) tl in
+      let l' =
+        Array.fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
+      let bl' = Array.map (f l') bl in
+      if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
+      then cstr
+      else mkFix (ln,(lna,tl',bl'))
+  | CoFix(ln,(lna,tl,bl)) ->
+      let tl' = Array.map (f l) tl in
+      let l' =
+        Array.fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
+      let bl' = Array.map (f l') bl in
+      if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
+      then cstr
+      else mkCoFix (ln,(lna,tl',bl'))
+
+(* [fold_constr_with_binders g f n acc c] folds [f n] on the immediate
+   subterms of [c] starting from [acc] and proceeding from left to
+   right according to the usual representation of the constructions as
+   [fold_constr] but it carries an extra data [n] (typically a lift
+   index) which is processed by [g] (which typically add 1 to [n]) at
+   each binder traversal; it is not recursive *)
+
+let fold_constr_with_binders g f n acc c = match kind_of_term c with
+  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
+    | Construct _) -> acc
+  | Cast (c,_, t) -> f n (f n acc c) t
+  | Prod (_,t,c) -> f (g n) (f n acc t) c
+  | Lambda (_,t,c) -> f (g n) (f n acc t) c
+  | LetIn (_,b,t,c) -> f (g n) (f n (f n acc b) t) c
+  | App (c,l) -> Array.fold_left (f n) (f n acc c) l
+  | Proj (p,c) -> f n acc c
+  | Evar (_,l) -> Array.fold_left (f n) acc l
+  | Case (_,p,c,bl) -> Array.fold_left (f n) (f n (f n acc p) c) bl
+  | Fix (_,(lna,tl,bl)) ->
+      let n' = iterate g (Array.length tl) n in
+      let fd = Array.map2 (fun t b -> (t,b)) tl bl in
+      Array.fold_left (fun acc (t,b) -> f n' (f n acc t) b) acc fd
+  | CoFix (_,(lna,tl,bl)) ->
+      let n' = iterate g (Array.length tl) n in
+      let fd = Array.map2 (fun t b -> (t,b)) tl bl in
+      Array.fold_left (fun acc (t,b) -> f n' (f n acc t) b) acc fd
+
+(* [iter_constr_with_full_binders g f acc c] iters [f acc] on the immediate
+   subterms of [c]; it carries an extra data [acc] which is processed by [g] at
+   each binder traversal; it is not recursive and the order with which
+   subterms are processed is not specified *)
+
+let iter_constr_with_full_binders g f l c = match kind_of_term c with
+  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
+    | Construct _) -> ()
+  | Cast (c,_, t) -> f l c; f l t
+  | Prod (na,t,c) -> f l t; f (g (na,None,t) l) c
+  | Lambda (na,t,c) -> f l t; f (g (na,None,t) l) c
+  | LetIn (na,b,t,c) -> f l b; f l t; f (g (na,Some b,t) l) c
+  | App (c,args) -> f l c; Array.iter (f l) args
+  | Proj (p,c) -> f l c
+  | Evar (_,args) -> Array.iter (f l) args
+  | Case (_,p,c,bl) -> f l p; f l c; Array.iter (f l) bl
+  | Fix (_,(lna,tl,bl)) ->
+      let l' = Array.fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
+      Array.iter (f l) tl;
+      Array.iter (f l') bl
+  | CoFix (_,(lna,tl,bl)) ->
+      let l' = Array.fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
+      Array.iter (f l) tl;
+      Array.iter (f l') bl
+
+(***************************)
+(* occurs check functions  *)
+(***************************)
+
+exception Occur
+
+let occur_meta c =
+  let rec occrec c = match kind_of_term c with
+    | Meta _ -> raise Occur
+    | _ -> iter_constr occrec c
+  in try occrec c; false with Occur -> true
+
+let occur_existential c =
+  let rec occrec c = match kind_of_term c with
+    | Evar _ -> raise Occur
+    | _ -> iter_constr occrec c
+  in try occrec c; false with Occur -> true
+
+let occur_meta_or_existential c =
+  let rec occrec c = match kind_of_term c with
+    | Evar _ -> raise Occur
+    | Meta _ -> raise Occur
+    | _ -> iter_constr occrec c
+  in try occrec c; false with Occur -> true
+
+let occur_evar n c =
+  let rec occur_rec c = match kind_of_term c with
+    | Evar (sp,_) when Evar.equal sp n -> raise Occur
+    | _ -> iter_constr occur_rec c
+  in
+  try occur_rec c; false with Occur -> true
+
+let occur_in_global env id constr =
+  let vars = vars_of_global env constr in
+  if Id.Set.mem id vars then raise Occur
+
+let occur_var env id c =
+  let rec occur_rec c =
+    match kind_of_term c with
+    | Var _ | Const _ | Ind _ | Construct _ -> occur_in_global env id c
+    | _ -> iter_constr occur_rec c
+  in
+  try occur_rec c; false with Occur -> true
+
+let occur_var_in_decl env hyp (_,c,typ) =
+  match c with
+    | None -> occur_var env hyp typ
+    | Some body ->
+        occur_var env hyp typ ||
+        occur_var env hyp body
+
+(* returns the list of free debruijn indices in a term *)
+
+let free_rels m =
+  let rec frec depth acc c = match kind_of_term c with
+    | Rel n       -> if n >= depth then Int.Set.add (n-depth+1) acc else acc
+    | _ -> fold_constr_with_binders succ frec depth acc c
+  in
+  frec 1 Int.Set.empty m
+
+(* collects all metavar occurences, in left-to-right order, preserving
+ * repetitions and all. *)
+
+let collect_metas c =
+  let rec collrec acc c =
+    match kind_of_term c with
+      | Meta mv -> List.add_set Int.equal mv acc
+      | _       -> fold_constr collrec acc c
+  in
+  List.rev (collrec [] c)
+
+(* collects all vars; warning: this is only visible vars, not dependencies in
+   all section variables; for the latter, use global_vars_set *)
+let collect_vars c =
+  let rec aux vars c = match kind_of_term c with
+  | Var id -> Id.Set.add id vars
+  | _ -> fold_constr aux vars c in
+  aux Id.Set.empty c
+
+(* Tests whether [m] is a subterm of [t]:
+   [m] is appropriately lifted through abstractions of [t] *)
+
+let dependent_main noevar univs m t =
+  let eqc x y = if univs then fst (Universes.eq_constr_universes x y) else eq_constr_nounivs x y in
+  let rec deprec m t =
+    if eqc m t then
+      raise Occur
+    else
+      match kind_of_term m, kind_of_term t with
+	| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
+	    deprec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
+	    CArray.Fun1.iter deprec m
+	      (Array.sub lt
+		(Array.length lm) ((Array.length lt) - (Array.length lm)))
+	| _, Cast (c,_,_) when noevar && isMeta c -> ()
+	| _, Evar _ when noevar -> ()
+	| _ -> iter_constr_with_binders (fun c -> lift 1 c) deprec m t
+  in
+  try deprec m t; false with Occur -> true
+
+let dependent = dependent_main false false
+let dependent_no_evar = dependent_main true false
+
+let dependent_univs = dependent_main false true
+let dependent_univs_no_evar = dependent_main true true
+
+let dependent_in_decl a (_,c,t) =
+  match c with
+    | None -> dependent a t
+    | Some body -> dependent a body || dependent a t
+
+let count_occurrences m t =
+  let n = ref 0 in
+  let rec countrec m t =
+    if eq_constr m t then
+      incr n
+    else
+      match kind_of_term m, kind_of_term t with
+	| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
+	    countrec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
+	    Array.iter (countrec m)
+	      (Array.sub lt
+		(Array.length lm) ((Array.length lt) - (Array.length lm)))
+	| _, Cast (c,_,_) when isMeta c -> ()
+	| _, Evar _ -> ()
+	| _ -> iter_constr_with_binders (lift 1) countrec m t
+  in
+  countrec m t;
+  !n
+
+(* Synonymous *)
+let occur_term = dependent
+
+let pop t = lift (-1) t
+
+(***************************)
+(*  bindings functions *)
+(***************************)
+
+type meta_type_map = (metavariable * types) list
+
+type meta_value_map = (metavariable * constr) list
+
+let rec subst_meta bl c =
+  match kind_of_term c with
+    | Meta i -> (try Int.List.assoc i bl with Not_found -> c)
+    | _ -> map_constr (subst_meta bl) c
+
+(* First utilities for avoiding telescope computation for subst_term *)
+
+let prefix_application eq_fun (k,c) (t : constr) =
+  let c' = collapse_appl c and t' = collapse_appl t in
+  match kind_of_term c', kind_of_term t' with
+    | App (f1,cl1), App (f2,cl2) ->
+	let l1 = Array.length cl1
+	and l2 = Array.length cl2 in
+	if l1 <= l2
+	   && eq_fun c' (mkApp (f2, Array.sub cl2 0 l1)) then
+	  Some (mkApp (mkRel k, Array.sub cl2 l1 (l2 - l1)))
+	else
+	  None
+    | _ -> None
+
+let my_prefix_application eq_fun (k,c) (by_c : constr) (t : constr) =
+  let c' = collapse_appl c and t' = collapse_appl t in
+  match kind_of_term c', kind_of_term t' with
+    | App (f1,cl1), App (f2,cl2) ->
+	let l1 = Array.length cl1
+	and l2 = Array.length cl2 in
+	if l1 <= l2
+	   && eq_fun c' (mkApp (f2, Array.sub cl2 0 l1)) then
+	  Some (mkApp ((lift k by_c), Array.sub cl2 l1 (l2 - l1)))
+	else
+	  None
+    | _ -> None
+
+(* Recognizing occurrences of a given subterm in a term: [subst_term c t]
+   substitutes [(Rel 1)] for all occurrences of term [c] in a term [t];
+   works if [c] has rels *)
+
+let subst_term_gen eq_fun c t =
+  let rec substrec (k,c as kc) t =
+    match prefix_application eq_fun kc t with
+      | Some x -> x
+      | None ->
+    if eq_fun c t then mkRel k
+    else
+      map_constr_with_binders (fun (k,c) -> (k+1,lift 1 c)) substrec kc t
+  in
+  substrec (1,c) t
+
+let subst_term = subst_term_gen eq_constr
+
+(* Recognizing occurrences of a given subterm in a term :
+   [replace_term c1 c2 t] substitutes [c2] for all occurrences of
+   term [c1] in a term [t]; works if [c1] and [c2] have rels *)
+
+let replace_term_gen eq_fun c by_c in_t =
+  let rec substrec (k,c as kc) t =
+    match my_prefix_application eq_fun kc by_c t with
+      | Some x -> x
+      | None ->
+    (if eq_fun c t then (lift k by_c) else
+      map_constr_with_binders (fun (k,c) -> (k+1,lift 1 c))
+	substrec kc t)
+  in
+  substrec (0,c) in_t
+
+let replace_term = replace_term_gen eq_constr
+
+let vars_of_env env =
+  let s =
+    Context.fold_named_context (fun (id,_,_) s -> Id.Set.add id s)
+      (named_context env) ~init:Id.Set.empty in
+  Context.fold_rel_context
+    (fun (na,_,_) s -> match na with Name id -> Id.Set.add id s | _ -> s)
+    (rel_context env) ~init:s
+
+let add_vname vars = function
+    Name id -> Id.Set.add id vars
+  | _ -> vars
+
+(*************************)
+(*   Names environments  *)
+(*************************)
+type names_context = Name.t list
+let add_name n nl = n::nl
+let lookup_name_of_rel p names =
+  try List.nth names (p-1)
+  with Invalid_argument _ | Failure _ -> raise Not_found
+let lookup_rel_of_name id names =
+  let rec lookrec n = function
+    | Anonymous :: l  -> lookrec (n+1) l
+    | (Name id') :: l -> if Id.equal id' id then n else lookrec (n+1) l
+    | []            -> raise Not_found
+  in
+  lookrec 1 names
+let empty_names_context = []
+
+let ids_of_rel_context sign =
+  Context.fold_rel_context
+    (fun (na,_,_) l -> match na with Name id -> id::l | Anonymous -> l)
+    sign ~init:[]
+
+let ids_of_named_context sign =
+  Context.fold_named_context (fun (id,_,_) idl -> id::idl) sign ~init:[]
+
+let ids_of_context env =
+  (ids_of_rel_context (rel_context env))
+  @ (ids_of_named_context (named_context env))
+
+
+let names_of_rel_context env =
+  List.map (fun (na,_,_) -> na) (rel_context env)
+
+let is_section_variable id =
+  try let _ = Global.lookup_named id in true
+  with Not_found -> false
+
+let isGlobalRef c =
+  match kind_of_term c with
+  | Const _ | Ind _ | Construct _ | Var _ -> true
+  | _ -> false
+
+let is_template_polymorphic env f =
+  match kind_of_term f with
+  | Ind ind -> Environ.template_polymorphic_pind ind env
+  | Const c -> Environ.template_polymorphic_pconstant c env
+  | _ -> false
+
+let base_sort_cmp pb s0 s1 =
+  match (s0,s1) with
+    | (Prop c1, Prop c2) -> c1 == Null || c2 == Pos  (* Prop <= Set *)
+    | (Prop c1, Type u)  -> pb == Reduction.CUMUL
+    | (Type u1, Type u2) -> true
+    | _ -> false
+
+(* eq_constr extended with universe erasure *)
+let compare_constr_univ f cv_pb t1 t2 =
+  match kind_of_term t1, kind_of_term t2 with
+      Sort s1, Sort s2 -> base_sort_cmp cv_pb s1 s2
+    | Prod (_,t1,c1), Prod (_,t2,c2) ->
+	f Reduction.CONV t1 t2 && f cv_pb c1 c2
+    | _ -> compare_constr (fun t1 t2 -> f Reduction.CONV t1 t2) t1 t2
+
+let rec constr_cmp cv_pb t1 t2 = compare_constr_univ constr_cmp cv_pb t1 t2
+
+let eq_constr t1 t2 = constr_cmp Reduction.CONV t1 t2
+
+(* App(c,[t1,...tn]) -> ([c,t1,...,tn-1],tn)
+   App(c,[||]) -> ([],c) *)
+let split_app c = match kind_of_term c with
+    App(c,l) ->
+      let len = Array.length l in
+      if Int.equal len 0 then ([],c) else
+	let last = Array.get l (len-1) in
+	let prev = Array.sub l 0 (len-1) in
+	c::(Array.to_list prev), last
+  | _ -> assert false
+
+type subst = (rel_context*constr) Evar.Map.t
+
+exception CannotFilter
+
+let filtering env cv_pb c1 c2 =
+  let evm = ref Evar.Map.empty in
+  let define cv_pb e1 ev c1 =
+    try let (e2,c2) = Evar.Map.find ev !evm in
+    let shift = List.length e1 - List.length e2 in
+    if constr_cmp cv_pb c1 (lift shift c2) then () else raise CannotFilter
+    with Not_found ->
+      evm := Evar.Map.add ev (e1,c1) !evm
+  in
+  let rec aux env cv_pb c1 c2 =
+    match kind_of_term c1, kind_of_term c2 with
+      | App _, App _ ->
+        let ((p1,l1),(p2,l2)) = (split_app c1),(split_app c2) in
+        let () = aux env cv_pb l1 l2 in
+        begin match p1, p2 with
+        | [], [] -> ()
+        | (h1 :: p1), (h2 :: p2) ->
+          aux env cv_pb (applistc h1 p1) (applistc h2 p2)
+        | _ -> assert false
+        end
+      | Prod (n,t1,c1), Prod (_,t2,c2) ->
+	  aux env cv_pb t1 t2;
+	  aux ((n,None,t1)::env) cv_pb c1 c2
+      | _, Evar (ev,_) -> define cv_pb env ev c1
+      | Evar (ev,_), _ -> define cv_pb env ev c2
+      | _ ->
+	  if compare_constr_univ
+	  (fun pb c1 c2 -> aux env pb c1 c2; true) cv_pb c1 c2 then ()
+	  else raise CannotFilter
+	  (* TODO: le reste des binders *)
+  in
+  aux env cv_pb c1 c2; !evm
+
+let decompose_prod_letin : constr -> int * rel_context * constr =
+  let rec prodec_rec i l c = match kind_of_term c with
+    | Prod (n,t,c)    -> prodec_rec (succ i) ((n,None,t)::l) c
+    | LetIn (n,d,t,c) -> prodec_rec (succ i) ((n,Some d,t)::l) c
+    | Cast (c,_,_)    -> prodec_rec i l c
+    | _               -> i,l,c in
+  prodec_rec 0 []
+
+let align_prod_letin c a : rel_context * constr =
+  let (lc,_,_) = decompose_prod_letin c in
+  let (la,l,a) = decompose_prod_letin a in
+  if not (la >= lc) then invalid_arg "align_prod_letin";
+  let (l1,l2) = Util.List.chop lc l in
+  l2,it_mkProd_or_LetIn a l1
+
+(* We reduce a series of head eta-redex or nothing at all   *)
+(* [x1:c1;...;xn:cn]@(f;a1...an;x1;...;xn) --> @(f;a1...an) *)
+(* Remplace 2 earlier buggish versions                      *)
+
+let rec eta_reduce_head c =
+  match kind_of_term c with
+    | Lambda (_,c1,c') ->
+	(match kind_of_term (eta_reduce_head c') with
+           | App (f,cl) ->
+               let lastn = (Array.length cl) - 1 in
+               if lastn < 0 then anomaly (Pp.str "application without arguments")
+               else
+                 (match kind_of_term cl.(lastn) with
+                    | Rel 1 ->
+			let c' =
+                          if Int.equal lastn 0 then f
+			  else mkApp (f, Array.sub cl 0 lastn)
+			in
+			if noccurn 1 c'
+                        then lift (-1) c'
+                        else c
+                    | _   -> c)
+           | _ -> c)
+    | _ -> c
+
+
+(* iterator on rel context *)
+let process_rel_context f env =
+  let sign = named_context_val env in
+  let rels = rel_context env in
+  let env0 = reset_with_named_context sign env in
+  Context.fold_rel_context f rels ~init:env0
+
+let assums_of_rel_context sign =
+  Context.fold_rel_context
+    (fun (na,c,t) l ->
+      match c with
+          Some _ -> l
+        | None -> (na, t)::l)
+    sign ~init:[]
+
+let map_rel_context_in_env f env sign =
+  let rec aux env acc = function
+    | d::sign ->
+	aux (push_rel d env) (map_rel_declaration (f env) d :: acc) sign
+    | [] ->
+	acc
+  in
+  aux env [] (List.rev sign)
+
+let map_rel_context_with_binders f sign =
+  let rec aux k = function
+    | d::sign -> map_rel_declaration (f k) d :: aux (k-1) sign
+    | [] -> []
+  in
+  aux (rel_context_length sign) sign
+
+let substl_rel_context l =
+  map_rel_context_with_binders (fun k -> substnl l (k-1))
+
+let lift_rel_context n =
+  map_rel_context_with_binders (liftn n)
+
+let smash_rel_context sign =
+  let rec aux acc = function
+  | [] -> acc
+  | (_,None,_ as d) :: l -> aux (d::acc) l
+  | (_,Some b,_) :: l ->
+      (* Quadratic in the number of let but there are probably a few of them *)
+      aux (List.rev (substl_rel_context [b] (List.rev acc))) l
+  in List.rev (aux [] sign)
+
+let adjust_subst_to_rel_context sign l =
+  let rec aux subst sign l =
+    match sign, l with
+    | (_,None,_)::sign', a::args' -> aux (a::subst) sign' args'
+    | (_,Some c,_)::sign', args' ->
+	aux (substl (List.rev subst) c :: subst) sign' args'
+    | [], [] -> List.rev subst
+    | _ -> anomaly (Pp.str "Instance and signature do not match")
+  in aux [] (List.rev sign) l
+
+let fold_named_context_both_sides f l ~init = List.fold_right_and_left f l init
+
+let rec mem_named_context id = function
+  | (id',_,_) :: _ when Id.equal id id' -> true
+  | _ :: sign -> mem_named_context id sign
+  | [] -> false
+
+let compact_named_context_reverse sign =
+  let compact l (i1,c1,t1) =
+    match l with
+    | [] -> [[i1],c1,t1]
+    | (l2,c2,t2)::q ->
+       if Option.equal Constr.equal c1 c2 && Constr.equal t1 t2
+       then (i1::l2,c2,t2)::q
+       else ([i1],c1,t1)::l
+  in Context.fold_named_context_reverse compact ~init:[] sign
+
+let compact_named_context sign = List.rev (compact_named_context_reverse sign)
+
+let clear_named_body id env =
+  let aux _ = function
+  | (id',Some c,t) when Id.equal id id' -> push_named (id,None,t)
+  | d -> push_named d in
+  fold_named_context aux env ~init:(reset_context env)
+
+let global_vars env ids = Id.Set.elements (global_vars_set env ids)
+
+let global_vars_set_of_decl env = function
+  | (_,None,t) -> global_vars_set env t
+  | (_,Some c,t) ->
+      Id.Set.union (global_vars_set env t)
+        (global_vars_set env c)
+
+let dependency_closure env sign hyps =
+  if Id.Set.is_empty hyps then [] else
+    let (_,lh) =
+      Context.fold_named_context_reverse
+        (fun (hs,hl) (x,_,_ as d) ->
+          if Id.Set.mem x hs then
+            (Id.Set.union (global_vars_set_of_decl env d) (Id.Set.remove x hs),
+            x::hl)
+          else (hs,hl))
+        ~init:(hyps,[])
+        sign in
+    List.rev lh
+
+(* Combinators on judgments *)
+
+let on_judgment f j = { uj_val = f j.uj_val; uj_type = f j.uj_type }
+let on_judgment_value f j = { j with uj_val = f j.uj_val }
+let on_judgment_type f j = { j with uj_type = f j.uj_type }
+
+(* Cut a context ctx in 2 parts (ctx1,ctx2) with ctx1 containing k
+     variables; skips let-in's *)
+let context_chop k ctx =
+  let rec chop_aux acc = function
+    | (0, l2) -> (List.rev acc, l2)
+    | (n, ((_,Some _,_ as h)::t)) -> chop_aux (h::acc) (n, t)
+    | (n, (h::t)) -> chop_aux (h::acc) (pred n, t)
+    | (_, []) -> anomaly (Pp.str "context_chop")
+  in chop_aux [] (k,ctx)
+
+(* Do not skip let-in's *)
+let env_rel_context_chop k env =
+  let rels = rel_context env in
+  let ctx1,ctx2 = List.chop k rels in
+  push_rel_context ctx2 (reset_with_named_context (named_context_val env) env),
+  ctx1
+
+(*******************************************)
+(* Functions to deal with impossible cases *)
+(*******************************************)
+let impossible_default_case = ref None
+
+let set_impossible_default_clause c = impossible_default_case := Some c
+
+let coq_unit_judge =
+  let na1 = Name (Id.of_string "A") in
+  let na2 = Name (Id.of_string "H") in
+  fun () ->
+    match !impossible_default_case with
+    | Some fn -> 
+        let (id,type_of_id), ctx = fn () in
+	  make_judge id type_of_id, ctx
+    | None ->
+	(* In case the constants id/ID are not defined *)
+	make_judge (mkLambda (na1,mkProp,mkLambda(na2,mkRel 1,mkRel 1)))
+                 (mkProd (na1,mkProp,mkArrow (mkRel 1) (mkRel 2))), 
+       Univ.ContextSet.empty
diff --git a/engine/termops.mli b/engine/termops.mli
new file mode 100644
index 000000000..2552c67e6
--- /dev/null
+++ b/engine/termops.mli
@@ -0,0 +1,244 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Pp
+open Names
+open Term
+open Context
+open Environ
+
+(** printers *)
+val print_sort : sorts -> std_ppcmds
+val pr_sort_family : sorts_family -> std_ppcmds
+val pr_fix : (constr -> std_ppcmds) -> fixpoint -> std_ppcmds
+
+(** debug printer: do not use to display terms to the casual user... *)
+val set_print_constr : (env -> constr -> std_ppcmds) -> unit
+val print_constr     : constr -> std_ppcmds
+val print_constr_env : env -> constr -> std_ppcmds
+val print_named_context : env -> std_ppcmds
+val pr_rel_decl : env -> rel_declaration -> std_ppcmds
+val print_rel_context : env -> std_ppcmds
+val print_env : env -> std_ppcmds
+
+(** about contexts *)
+val push_rel_assum : Name.t * types -> env -> env
+val push_rels_assum : (Name.t * types) list -> env -> env
+val push_named_rec_types : Name.t array * types array * 'a -> env -> env
+
+val lookup_rel_id : Id.t -> rel_context -> int * constr option * types
+(** Associates the contents of an identifier in a [rel_context]. Raise
+    [Not_found] if there is no such identifier. *)
+
+(** Functions that build argument lists matching a block of binders or a context.
+    [rel_vect n m] builds [|Rel (n+m);...;Rel(n+1)|]
+    [extended_rel_vect n ctx] extends the [ctx] context of length [m]
+    with [n] elements.
+*)
+val rel_vect : int -> int -> constr array
+val rel_list : int -> int -> constr list
+val extended_rel_list : int -> rel_context -> constr list
+val extended_rel_vect : int -> rel_context -> constr array
+
+(** iterators/destructors on terms *)
+val mkProd_or_LetIn : rel_declaration -> types -> types
+val mkProd_wo_LetIn : rel_declaration -> types -> types
+val it_mkProd : types -> (Name.t * types) list -> types
+val it_mkLambda : constr -> (Name.t * types) list -> constr
+val it_mkProd_or_LetIn : types -> rel_context -> types
+val it_mkProd_wo_LetIn : types -> rel_context -> types
+val it_mkLambda_or_LetIn : constr -> rel_context -> constr
+val it_mkNamedProd_or_LetIn : types -> named_context -> types
+val it_mkNamedProd_wo_LetIn : types -> named_context -> types
+val it_mkNamedLambda_or_LetIn : constr -> named_context -> constr
+
+(* Ad hoc version reinserting letin, assuming the body is defined in
+   the context where the letins are expanded *)
+val it_mkLambda_or_LetIn_from_no_LetIn : constr -> rel_context -> constr
+
+(** {6 Generic iterators on constr} *)
+
+val map_constr_with_named_binders :
+  (Name.t -> 'a -> 'a) ->
+  ('a -> constr -> constr) -> 'a -> constr -> constr
+val map_constr_with_binders_left_to_right :
+  (rel_declaration -> 'a -> 'a) ->
+  ('a -> constr -> constr) ->
+    'a -> constr -> constr
+val map_constr_with_full_binders :
+  (rel_declaration -> 'a -> 'a) ->
+  ('a -> constr -> constr) -> 'a -> constr -> constr
+
+(** [fold_constr_with_binders g f n acc c] folds [f n] on the immediate
+   subterms of [c] starting from [acc] and proceeding from left to
+   right according to the usual representation of the constructions as
+   [fold_constr] but it carries an extra data [n] (typically a lift
+   index) which is processed by [g] (which typically add 1 to [n]) at
+   each binder traversal; it is not recursive *)
+
+val fold_constr_with_binders :
+  ('a -> 'a) -> ('a -> 'b -> constr -> 'b) -> 'a -> 'b -> constr -> 'b
+
+val iter_constr_with_full_binders :
+  (rel_declaration -> 'a -> 'a) -> ('a -> constr -> unit) -> 'a ->
+    constr -> unit
+
+(**********************************************************************)
+
+val strip_head_cast : constr -> constr
+val drop_extra_implicit_args : constr -> constr
+
+(** occur checks *)
+exception Occur
+val occur_meta : types -> bool
+val occur_existential : types -> bool
+val occur_meta_or_existential : types -> bool
+val occur_evar : existential_key -> types -> bool
+val occur_var : env -> Id.t -> types -> bool
+val occur_var_in_decl :
+  env ->
+  Id.t -> 'a * types option * types -> bool
+val free_rels : constr -> Int.Set.t
+
+(** [dependent m t] tests whether [m] is a subterm of [t] *)
+val dependent : constr -> constr -> bool
+val dependent_no_evar : constr -> constr -> bool
+val dependent_univs : constr -> constr -> bool
+val dependent_univs_no_evar : constr -> constr -> bool
+val dependent_in_decl : constr -> named_declaration -> bool
+val count_occurrences : constr -> constr -> int
+val collect_metas : constr -> int list
+val collect_vars : constr -> Id.Set.t (** for visible vars only *)
+val occur_term : constr -> constr -> bool (** Synonymous
+ of dependent 
+   Substitution of metavariables *)
+type meta_value_map = (metavariable * constr) list
+val subst_meta : meta_value_map -> constr -> constr
+
+(** Type assignment for metavariables *)
+type meta_type_map = (metavariable * types) list
+
+(** [pop c] lifts by -1 the positive indexes in [c] *)
+val pop : constr -> constr
+
+(** {6 ... } *)
+(** Substitution of an arbitrary large term. Uses equality modulo
+   reduction of let *)
+
+(** [subst_term_gen eq d c] replaces [Rel 1] by [d] in [c] using [eq]
+   as equality *)
+val subst_term_gen :
+  (constr -> constr -> bool) -> constr -> constr -> constr
+
+(** [replace_term_gen eq d e c] replaces [d] by [e] in [c] using [eq]
+   as equality *)
+val replace_term_gen :
+  (constr -> constr -> bool) ->
+    constr -> constr -> constr -> constr
+
+(** [subst_term d c] replaces [Rel 1] by [d] in [c] *)
+val subst_term : constr -> constr -> constr
+
+(** [replace_term d e c] replaces [d] by [e] in [c] *)
+val replace_term : constr -> constr -> constr -> constr
+
+(** Alternative term equalities *)
+val base_sort_cmp : Reduction.conv_pb -> sorts -> sorts -> bool
+val compare_constr_univ : (Reduction.conv_pb -> constr -> constr -> bool) ->
+  Reduction.conv_pb -> constr -> constr -> bool
+val constr_cmp : Reduction.conv_pb -> constr -> constr -> bool
+val eq_constr : constr -> constr -> bool (* FIXME rename: erases universes*)
+
+val eta_reduce_head : constr -> constr
+
+exception CannotFilter
+
+(** Lightweight first-order filtering procedure. Unification
+   variables ar represented by (untyped) Evars.
+   [filtering c1 c2] returns the substitution n'th evar ->
+   (context,term), or raises [CannotFilter].
+   Warning: Outer-kernel sort subtyping are taken into account: c1 has
+   to be smaller than c2 wrt. sorts. *)
+type subst = (rel_context*constr) Evar.Map.t
+val filtering : rel_context -> Reduction.conv_pb -> constr -> constr -> subst
+
+val decompose_prod_letin : constr -> int * rel_context * constr
+val align_prod_letin : constr -> constr -> rel_context * constr
+
+(** Get the last arg of a constr intended to be an application *)
+val last_arg : constr -> constr
+
+(** Force the decomposition of a term as an applicative one *)
+val decompose_app_vect : constr -> constr * constr array
+
+val adjust_app_list_size : constr -> constr list -> constr -> constr list ->
+  (constr * constr list * constr * constr list)
+val adjust_app_array_size : constr -> constr array -> constr -> constr array ->
+  (constr * constr array * constr * constr array)
+
+(** name contexts *)
+type names_context = Name.t list
+val add_name : Name.t -> names_context -> names_context
+val lookup_name_of_rel : int -> names_context -> Name.t
+val lookup_rel_of_name : Id.t -> names_context -> int
+val empty_names_context : names_context
+val ids_of_rel_context : rel_context -> Id.t list
+val ids_of_named_context : named_context -> Id.t list
+val ids_of_context : env -> Id.t list
+val names_of_rel_context : env -> names_context
+
+val context_chop : int -> rel_context -> rel_context * rel_context
+val env_rel_context_chop : int -> env -> env * rel_context
+
+(** Set of local names *)
+val vars_of_env: env -> Id.Set.t
+val add_vname : Id.Set.t -> Name.t -> Id.Set.t
+
+(** other signature iterators *)
+val process_rel_context : (rel_declaration -> env -> env) -> env -> env
+val assums_of_rel_context : rel_context -> (Name.t * constr) list
+val lift_rel_context : int -> rel_context -> rel_context
+val substl_rel_context : constr list -> rel_context -> rel_context
+val smash_rel_context : rel_context -> rel_context (** expand lets in context *)
+val adjust_subst_to_rel_context : rel_context -> constr list -> constr list
+val map_rel_context_in_env :
+  (env -> constr -> constr) -> env -> rel_context -> rel_context
+val map_rel_context_with_binders :
+  (int -> constr -> constr) -> rel_context -> rel_context
+val fold_named_context_both_sides :
+  ('a -> named_declaration -> named_declaration list -> 'a) ->
+    named_context -> init:'a -> 'a
+val mem_named_context : Id.t -> named_context -> bool
+val compact_named_context : named_context -> named_list_context
+val compact_named_context_reverse : named_context -> named_list_context
+
+val clear_named_body : Id.t -> env -> env
+
+val global_vars : env -> constr -> Id.t list
+val global_vars_set_of_decl : env -> named_declaration -> Id.Set.t
+
+(** Gives an ordered list of hypotheses, closed by dependencies,
+   containing a given set *)
+val dependency_closure : env -> named_context -> Id.Set.t -> Id.t list
+
+(** Test if an identifier is the basename of a global reference *)
+val is_section_variable : Id.t -> bool
+
+val isGlobalRef : constr -> bool
+
+val is_template_polymorphic : env -> constr -> bool
+
+(** Combinators on judgments *)
+
+val on_judgment       : (types -> types) -> unsafe_judgment -> unsafe_judgment
+val on_judgment_value : (types -> types) -> unsafe_judgment -> unsafe_judgment
+val on_judgment_type  : (types -> types) -> unsafe_judgment -> unsafe_judgment
+
+(** {6 Functions to deal with impossible cases } *)
+val set_impossible_default_clause : (unit -> (constr * types) Univ.in_universe_context_set) -> unit
+val coq_unit_judge : unit -> unsafe_judgment Univ.in_universe_context_set