Moving Evarutil and Proofview to engine/

5 files changed, 2746 insertions, 0 deletions

diff --git a/engine/engine.mllib b/engine/engine.mllib
index 7197a2583..70b74edca 100644
--- a/engine/engine.mllib
+++ b/engine/engine.mllib
@@ -5,3 +5,5 @@ UState
 Evd
 Sigma
 Proofview_monad
+Evarutil
+Proofview
diff --git a/engine/evarutil.ml b/engine/evarutil.ml
new file mode 100644
index 000000000..2bd67dcdc
--- /dev/null
+++ b/engine/evarutil.ml
@@ -0,0 +1,723 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Errors
+open Util
+open Pp
+open Names
+open Term
+open Vars
+open Termops
+open Namegen
+open Pre_env
+open Environ
+open Evd
+open Sigma.Notations
+
+let safe_evar_value sigma ev =
+  try Some (Evd.existential_value sigma ev)
+  with NotInstantiatedEvar | Not_found -> None
+
+(** Combinators *)
+
+let evd_comb0 f evdref =
+  let (evd',x) = f !evdref in
+    evdref := evd';
+    x
+
+let evd_comb1 f evdref x =
+  let (evd',y) = f !evdref x in
+    evdref := evd';
+    y
+
+let evd_comb2 f evdref x y =
+  let (evd',z) = f !evdref x y in
+    evdref := evd';
+    z
+
+let e_new_global evdref x = 
+  evd_comb1 (Evd.fresh_global (Global.env())) evdref x
+
+let new_global evd x = 
+  Sigma.fresh_global (Global.env()) evd x
+
+(****************************************************)
+(* Expanding/testing/exposing existential variables *)
+(****************************************************)
+
+(* flush_and_check_evars fails if an existential is undefined *)
+
+exception Uninstantiated_evar of existential_key
+
+let rec flush_and_check_evars sigma c =
+  match kind_of_term c with
+  | Evar (evk,_ as ev) ->
+      (match existential_opt_value sigma ev with
+       | None -> raise (Uninstantiated_evar evk)
+       | Some c -> flush_and_check_evars sigma c)
+  | _ -> map_constr (flush_and_check_evars sigma) c
+
+(* let nf_evar_key = Profile.declare_profile "nf_evar"  *)
+(* let nf_evar = Profile.profile2 nf_evar_key Reductionops.nf_evar *)
+
+let rec whd_evar sigma c =
+  match kind_of_term c with
+    | Evar ev ->
+        let (evk, args) = ev in
+        let args = Array.map (fun c -> whd_evar sigma c) args in
+        (match safe_evar_value sigma (evk, args) with
+            Some c -> whd_evar sigma c
+          | None -> c)
+    | Sort (Type u) -> 
+      let u' = Evd.normalize_universe sigma u in
+	if u' == u then c else mkSort (Sorts.sort_of_univ u')
+    | Const (c', u) when not (Univ.Instance.is_empty u) -> 
+      let u' = Evd.normalize_universe_instance sigma u in
+	if u' == u then c else mkConstU (c', u')
+    | Ind (i, u) when not (Univ.Instance.is_empty u) -> 
+      let u' = Evd.normalize_universe_instance sigma u in
+	if u' == u then c else mkIndU (i, u')
+    | Construct (co, u) when not (Univ.Instance.is_empty u) ->
+      let u' = Evd.normalize_universe_instance sigma u in
+	if u' == u then c else mkConstructU (co, u')
+    | _ -> c
+
+let rec nf_evar sigma t = Constr.map (fun t -> nf_evar sigma t) (whd_evar sigma t)
+
+let j_nf_evar sigma j =
+  { uj_val = nf_evar sigma j.uj_val;
+    uj_type = nf_evar sigma j.uj_type }
+let jl_nf_evar sigma jl = List.map (j_nf_evar sigma) jl
+let jv_nf_evar sigma = Array.map (j_nf_evar sigma)
+let tj_nf_evar sigma {utj_val=v;utj_type=t} =
+  {utj_val=nf_evar sigma v;utj_type=t}
+
+let nf_evars_universes evm =
+  Universes.nf_evars_and_universes_opt_subst (safe_evar_value evm) 
+    (Evd.universe_subst evm)
+    
+let nf_evars_and_universes evm =
+  let evm = Evd.nf_constraints evm in
+    evm, nf_evars_universes evm
+
+let e_nf_evars_and_universes evdref =
+  evdref := Evd.nf_constraints !evdref;
+  nf_evars_universes !evdref, Evd.universe_subst !evdref
+
+let nf_evar_map_universes evm =
+  let evm = Evd.nf_constraints evm in
+  let subst = Evd.universe_subst evm in
+    if Univ.LMap.is_empty subst then evm, nf_evar evm
+    else
+      let f = nf_evars_universes evm in
+	Evd.raw_map (fun _ -> map_evar_info f) evm, f
+
+let nf_named_context_evar sigma ctx =
+  Context.Named.map (nf_evar sigma) ctx
+
+let nf_rel_context_evar sigma ctx =
+  Context.Rel.map (nf_evar sigma) ctx
+
+let nf_env_evar sigma env =
+  let nc' = nf_named_context_evar sigma (Environ.named_context env) in
+  let rel' = nf_rel_context_evar sigma (Environ.rel_context env) in
+    push_rel_context rel' (reset_with_named_context (val_of_named_context nc') env)
+
+let nf_evar_info evc info = map_evar_info (nf_evar evc) info
+
+let nf_evar_map evm =
+  Evd.raw_map (fun _ evi -> nf_evar_info evm evi) evm
+
+let nf_evar_map_undefined evm =
+  Evd.raw_map_undefined (fun _ evi -> nf_evar_info evm evi) evm
+
+(*-------------------*)
+(* Auxiliary functions for the conversion algorithms modulo evars
+ *)
+
+(* A probably faster though more approximative variant of
+   [has_undefined (nf_evar c)]: instances are not substituted and
+   maybe an evar occurs in an instance and it would disappear by
+   instantiation *)
+
+let has_undefined_evars evd t =
+  let rec has_ev t =
+    match kind_of_term t with
+    | Evar (ev,args) ->
+        (match evar_body (Evd.find evd ev) with
+        | Evar_defined c ->
+            has_ev c; Array.iter has_ev args
+        | Evar_empty ->
+	    raise NotInstantiatedEvar)
+    | _ -> iter_constr has_ev t in
+  try let _ = has_ev t in false
+  with (Not_found | NotInstantiatedEvar) -> true
+
+let is_ground_term evd t =
+  not (has_undefined_evars evd t)
+
+let is_ground_env evd env =
+  let open Context.Rel.Declaration in
+  let is_ground_rel_decl = function
+    | LocalDef (_,b,_) -> is_ground_term evd b
+    | _ -> true in
+  let open Context.Named.Declaration in
+  let is_ground_named_decl = function
+    | LocalDef (_,b,_) -> is_ground_term evd b
+    | _ -> true in
+  List.for_all is_ground_rel_decl (rel_context env) &&
+  List.for_all is_ground_named_decl (named_context env)
+
+(* Memoization is safe since evar_map and environ are applicative
+   structures *)
+let memo f =
+  let m = ref None in
+  fun x y -> match !m with
+  | Some (x', y', r) when x == x' && y == y' -> r
+  | _ -> let r = f x y in m := Some (x, y, r); r
+
+let is_ground_env = memo is_ground_env
+
+(* Return the head evar if any *)
+
+exception NoHeadEvar
+
+let head_evar =
+  let rec hrec c = match kind_of_term c with
+    | Evar (evk,_)   -> evk
+    | Case (_,_,c,_) -> hrec c
+    | App (c,_)      -> hrec c
+    | Cast (c,_,_)   -> hrec c
+    | _              -> raise NoHeadEvar
+  in
+  hrec
+
+(* Expand head evar if any (currently consider only applications but I
+   guess it should consider Case too) *)
+
+let whd_head_evar_stack sigma c =
+  let rec whrec (c, l as s) =
+    match kind_of_term c with
+      | Evar (evk,args as ev) ->
+        let v =
+          try Some (existential_value sigma ev)
+          with NotInstantiatedEvar | Not_found  -> None in
+        begin match v with
+        | None -> s
+        | Some c -> whrec (c, l)
+        end
+      | Cast (c,_,_) -> whrec (c, l)
+      | App (f,args) -> whrec (f, args :: l)
+      | _ -> s
+  in
+  whrec (c, [])
+
+let whd_head_evar sigma c =
+  let (f, args) = whd_head_evar_stack sigma c in
+  (** optim: don't reallocate if empty/singleton *)
+  match args with
+  | [] -> f
+  | [arg] -> mkApp (f, arg)
+  | _ -> mkApp (f, Array.concat args)
+
+(**********************)
+(* Creating new metas *)
+(**********************)
+
+let meta_counter_summary_name = "meta counter"
+
+(* Generator of metavariables *)
+let new_meta =
+  let meta_ctr = Summary.ref 0 ~name:meta_counter_summary_name in
+  fun () -> incr meta_ctr; !meta_ctr
+
+let mk_new_meta () = mkMeta(new_meta())
+
+(* The list of non-instantiated existential declarations (order is important) *)
+
+let non_instantiated sigma =
+  let listev = Evd.undefined_map sigma in
+  Evar.Map.smartmap (fun evi -> nf_evar_info sigma evi) listev
+
+(************************)
+(* Manipulating filters *)
+(************************)
+
+let make_pure_subst evi args =
+  let open Context.Named.Declaration in
+  snd (List.fold_right
+    (fun decl (args,l) ->
+      match args with
+        | a::rest -> (rest, (get_id decl, a)::l)
+        | _ -> anomaly (Pp.str "Instance does not match its signature"))
+    (evar_filtered_context evi) (Array.rev_to_list args,[]))
+
+(*------------------------------------*
+ * functional operations on evar sets *
+ *------------------------------------*)
+
+(* [push_rel_context_to_named_context] builds the defining context and the
+ * initial instance of an evar. If the evar is to be used in context
+ *
+ * Gamma =  a1     ...    an xp      ...       x1
+ *          \- named part -/ \- de Bruijn part -/
+ *
+ * then the x1...xp are turned into variables so that the evar is declared in
+ * context
+ *
+ *          a1     ...    an xp      ...       x1
+ *          \----------- named part ------------/
+ *
+ * but used applied to the initial instance "a1 ... an Rel(p) ... Rel(1)"
+ * so that ev[a1:=a1 ... an:=an xp:=Rel(p) ... x1:=Rel(1)] is correctly typed
+ * in context Gamma.
+ *
+ * Remark 1: The instance is reverted in practice (i.e. Rel(1) comes first)
+ * Remark 2: If some of the ai or xj are definitions, we keep them in the
+ *   instance. This is necessary so that no unfolding of local definitions
+ *   happens when inferring implicit arguments (consider e.g. the problem
+ *   "x:nat; x':=x; f:forall y, y=y -> Prop |- f _ (refl_equal x')" which
+ *   produces the equation "?y[x,x']=?y[x,x']" =? "x'=x'": we want
+ *   the hole to be instantiated by x', not by x (which would have been
+ *   the case in [invert_definition] if x' had disappeared from the instance).
+ *   Note that at any time, if, in some context env, the instance of
+ *   declaration x:A is t and the instance of definition x':=phi(x) is u, then
+ *   we have the property that u and phi(t) are convertible in env.
+ *)
+
+let subst2 subst vsubst c =
+  substl subst (replace_vars vsubst c)
+
+let push_rel_context_to_named_context env typ =
+  (* compute the instances relative to the named context and rel_context *)
+  let open Context.Named.Declaration in
+  let ids = List.map get_id (named_context env) in
+  let inst_vars = List.map mkVar ids in
+  let inst_rels = List.rev (rel_list 0 (nb_rel env)) in
+  let replace_var_named_declaration id0 id decl =
+    let id' = get_id decl in
+    let id' = if Id.equal id0 id' then id else id' in
+    let vsubst = [id0 , mkVar id] in
+    decl |> set_id id' |> map_constr (replace_vars vsubst)
+  in
+  let replace_var_named_context id0 id  env =
+    let nc = Environ.named_context env in
+    let nc' = List.map (replace_var_named_declaration id0 id) nc in
+    Environ.reset_with_named_context (val_of_named_context nc') env
+  in
+  let extract_if_neq id = function
+    | Anonymous -> None
+    | Name id' when id_ord id id' = 0 -> None
+    | Name id' -> Some id'
+  in
+  (* move the rel context to a named context and extend the named instance *)
+  (* with vars of the rel context *)
+  (* We do keep the instances corresponding to local definition (see above) *)
+  let (subst, vsubst, _, env) =
+    Context.Rel.fold_outside
+      (fun decl (subst, vsubst, avoid, env) ->
+        let open Context.Rel.Declaration in
+        let na = get_name decl in
+	let c = get_value decl in
+	let t = get_type decl in
+        let open Context.Named.Declaration in
+        let id =
+          (* ppedrot: we want to infer nicer names for the refine tactic, but
+             keeping at the same time backward compatibility in other code
+             using this function. For now, we only attempt to preserve the
+             old behaviour of Program, but ultimately, one should do something
+             about this whole name generation problem. *)
+          if Flags.is_program_mode () then next_name_away na avoid
+          else next_ident_away (id_of_name_using_hdchar env t na) avoid
+        in
+        match extract_if_neq id na with
+        | Some id0 when not (is_section_variable id0) ->
+            (* spiwack: if [id<>id0], rather than introducing a new
+               binding named [id], we will keep [id0] (the name given
+               by the user) and rename [id0] into [id] in the named
+               context. Unless [id] is a section variable. *)
+            let subst = List.map (replace_vars [id0,mkVar id]) subst in
+            let vsubst = (id0,mkVar id)::vsubst in
+            let d = match c with
+              | None -> LocalAssum (id0, subst2 subst vsubst t)
+              | Some c -> LocalDef (id0, subst2 subst vsubst c, subst2 subst vsubst t)
+            in
+            let env = replace_var_named_context id0  id env in
+            (mkVar id0 :: subst, vsubst, id::avoid, push_named d env)
+        | _ ->
+            (* spiwack: if [id0] is a section variable renaming it is
+               incorrect. We revert to a less robust behaviour where
+               the new binder has name [id]. Which amounts to the same
+               behaviour than when [id=id0]. *)
+            let d = match c with
+              | None -> LocalAssum (id, subst2 subst vsubst t)
+              | Some c -> LocalDef (id, subst2 subst vsubst c, subst2 subst vsubst t)
+            in
+	    (mkVar id :: subst, vsubst, id::avoid, push_named d env)
+      )
+      (rel_context env) ~init:([], [], ids, env) in
+  (named_context_val env, subst2 subst vsubst typ, inst_rels@inst_vars, subst, vsubst)
+
+(*------------------------------------*
+ * Entry points to define new evars   *
+ *------------------------------------*)
+
+let default_source = (Loc.ghost,Evar_kinds.InternalHole)
+
+let restrict_evar evd evk filter candidates =
+  let evd = Sigma.to_evar_map evd in
+  let evd, evk' = Evd.restrict evk filter ?candidates evd in
+  Sigma.Unsafe.of_pair (evk', Evd.declare_future_goal evk' evd)
+
+let new_pure_evar_full evd evi =
+  let evd = Sigma.to_evar_map evd in
+  let (evd, evk) = Evd.new_evar evd evi in
+  let evd = Evd.declare_future_goal evk evd in
+  Sigma.Unsafe.of_pair (evk, evd)
+
+let new_pure_evar sign evd ?(src=default_source) ?(filter = Filter.identity) ?candidates ?(store = Store.empty) ?naming ?(principal=false) typ =
+  let evd = Sigma.to_evar_map evd in
+  let default_naming = Misctypes.IntroAnonymous in
+  let naming = Option.default default_naming naming in
+  let evi = {
+    evar_hyps = sign;
+    evar_concl = typ;
+    evar_body = Evar_empty;
+    evar_filter = filter;
+    evar_source = src;
+    evar_candidates = candidates;
+    evar_extra = store; }
+  in
+  let (evd, newevk) = Evd.new_evar evd ~naming evi in
+  let evd =
+    if principal then Evd.declare_principal_goal newevk evd
+    else Evd.declare_future_goal newevk evd
+  in
+  Sigma.Unsafe.of_pair (newevk, evd)
+
+let new_evar_instance sign evd typ ?src ?filter ?candidates ?store ?naming ?principal instance =
+  assert (not !Flags.debug ||
+            List.distinct (ids_of_named_context (named_context_of_val sign)));
+  let Sigma (newevk, evd, p) = new_pure_evar sign evd ?src ?filter ?candidates ?store ?naming ?principal typ in
+  Sigma (mkEvar (newevk,Array.of_list instance), evd, p)
+
+(* [new_evar] declares a new existential in an env env with type typ *)
+(* Converting the env into the sign of the evar to define *)
+let new_evar env evd ?src ?filter ?candidates ?store ?naming ?principal typ =
+  let sign,typ',instance,subst,vsubst = push_rel_context_to_named_context env typ in
+  let candidates = Option.map (List.map (subst2 subst vsubst)) candidates in
+  let instance =
+    match filter with
+    | None -> instance
+    | Some filter -> Filter.filter_list filter instance in
+  new_evar_instance sign evd typ' ?src ?filter ?candidates ?store ?naming ?principal instance
+
+let new_evar_unsafe env evd ?src ?filter ?candidates ?store ?naming ?principal typ =
+  let evd = Sigma.Unsafe.of_evar_map evd in
+  let Sigma (evk, evd, _) = new_evar env evd ?src ?filter ?candidates ?store ?naming ?principal typ in
+  (Sigma.to_evar_map evd, evk)
+
+let new_type_evar env evd ?src ?filter ?naming ?principal rigid =
+  let Sigma (s, evd', p) = Sigma.new_sort_variable rigid evd in
+  let Sigma (e, evd', q) = new_evar env evd' ?src ?filter ?naming ?principal (mkSort s) in
+  Sigma ((e, s), evd', p +> q)
+
+let e_new_type_evar env evdref ?src ?filter ?naming ?principal rigid =
+  let sigma = Sigma.Unsafe.of_evar_map !evdref in
+  let Sigma (c, sigma, _) = new_type_evar env sigma ?src ?filter ?naming ?principal rigid in
+  let sigma = Sigma.to_evar_map sigma in
+    evdref := sigma;
+    c
+
+let new_Type ?(rigid=Evd.univ_flexible) env evd = 
+  let Sigma (s, sigma, p) = Sigma.new_sort_variable rigid evd in
+  Sigma (mkSort s, sigma, p)
+
+let e_new_Type ?(rigid=Evd.univ_flexible) env evdref =
+  let evd', s = new_sort_variable rigid !evdref in
+    evdref := evd'; mkSort s
+
+  (* The same using side-effect *)
+let e_new_evar env evdref ?(src=default_source) ?filter ?candidates ?store ?naming ?principal ty =
+  let (evd',ev) = new_evar_unsafe env !evdref ~src:src ?filter ?candidates ?store ?naming ?principal ty in
+  evdref := evd';
+  ev
+
+(* This assumes an evar with identity instance and generalizes it over only
+   the De Bruijn part of the context *)
+let generalize_evar_over_rels sigma (ev,args) =
+  let evi = Evd.find sigma ev in
+  let sign = named_context_of_val evi.evar_hyps in
+  List.fold_left2
+    (fun (c,inst as x) a d ->
+      if isRel a then (mkNamedProd_or_LetIn d c,a::inst) else x)
+     (evi.evar_concl,[]) (Array.to_list args) sign
+
+(************************************)
+(* Removing a dependency in an evar *)
+(************************************)
+
+type clear_dependency_error =
+| OccurHypInSimpleClause of Id.t option
+| EvarTypingBreak of existential
+
+exception ClearDependencyError of Id.t * clear_dependency_error
+
+let cleared = Store.field ()
+
+exception Depends of Id.t
+
+let rec check_and_clear_in_constr env evdref err ids c =
+  (* returns a new constr where all the evars have been 'cleaned'
+     (ie the hypotheses ids have been removed from the contexts of
+     evars) *)
+  let check id' =
+    if Id.Set.mem id' ids then
+      raise (ClearDependencyError (id',err))
+  in
+    match kind_of_term c with
+      | Var id' ->
+	  check id'; c
+
+      | ( Const _ | Ind _ | Construct _ ) ->
+          let vars = Environ.vars_of_global env c in
+            Id.Set.iter check vars; c
+
+      | Evar (evk,l as ev) ->
+	  if Evd.is_defined !evdref evk then
+	    (* If evk is already defined we replace it by its definition *)
+	    let nc = whd_evar !evdref c in
+	      (check_and_clear_in_constr env evdref err ids nc)
+	  else
+	    (* We check for dependencies to elements of ids in the
+	       evar_info corresponding to e and in the instance of
+	       arguments. Concurrently, we build a new evar
+	       corresponding to e where hypotheses of ids have been
+	       removed *)
+	    let evi = Evd.find_undefined !evdref evk in
+	    let ctxt = Evd.evar_filtered_context evi in
+	    let (rids,filter) =
+              List.fold_right2
+                (fun h a (ri,filter) ->
+                  try
+                  (* Check if some id to clear occurs in the instance
+                     a of rid in ev and remember the dependency *)
+                    let check id = if Id.Set.mem id ids then raise (Depends id) in
+                    let () = Id.Set.iter check (collect_vars a) in
+                  (* Check if some rid to clear in the context of ev
+                     has dependencies in another hyp of the context of ev
+                     and transitively remember the dependency *)
+                    let check id _ =
+                      if occur_var_in_decl (Global.env ()) id h
+                      then raise (Depends id)
+                    in
+                    let () = Id.Map.iter check ri in
+                  (* No dependency at all, we can keep this ev's context hyp *)
+                    (ri, true::filter)
+                  with Depends id -> let open Context.Named.Declaration in
+                                     (Id.Map.add (get_id h) id ri, false::filter))
+		ctxt (Array.to_list l) (Id.Map.empty,[]) in
+	    (* Check if some rid to clear in the context of ev has dependencies
+	       in the type of ev and adjust the source of the dependency *)
+	    let _nconcl =
+	      try
+                let nids = Id.Map.domain rids in
+                check_and_clear_in_constr env evdref (EvarTypingBreak ev) nids (evar_concl evi)
+	      with ClearDependencyError (rid,err) ->
+		raise (ClearDependencyError (Id.Map.find rid rids,err)) in
+
+            if Id.Map.is_empty rids then c
+            else
+              let origfilter = Evd.evar_filter evi in
+              let filter = Evd.Filter.apply_subfilter origfilter filter in
+              let evd = Sigma.Unsafe.of_evar_map !evdref in
+              let Sigma (_, evd, _) = restrict_evar evd evk filter None in
+              let evd = Sigma.to_evar_map evd in
+              evdref := evd;
+	    (* spiwack: hacking session to mark the old [evk] as having been "cleared" *)
+	      let evi = Evd.find !evdref evk in
+	      let extra = evi.evar_extra in
+	      let extra' = Store.set extra cleared true in
+	      let evi' = { evi with evar_extra = extra' } in
+	      evdref := Evd.add !evdref evk evi' ;
+	    (* spiwack: /hacking session *)
+              whd_evar !evdref c
+
+      | _ -> map_constr (check_and_clear_in_constr env evdref err ids) c
+
+let clear_hyps_in_evi_main env evdref hyps terms ids =
+  (* clear_hyps_in_evi erases hypotheses ids in hyps, checking if some
+     hypothesis does not depend on a element of ids, and erases ids in
+     the contexts of the evars occurring in evi *)
+  let terms =
+    List.map (check_and_clear_in_constr env evdref (OccurHypInSimpleClause None) ids) terms in
+  let nhyps =
+    let open Context.Named.Declaration in
+    let check_context decl =
+      let err = OccurHypInSimpleClause (Some (get_id decl)) in
+      map_constr (check_and_clear_in_constr env evdref err ids) decl
+    in
+    let check_value vk = match force_lazy_val vk with
+    | None -> vk
+    | Some (_, d) ->
+      if (Id.Set.for_all (fun e -> not (Id.Set.mem e d)) ids) then
+        (* v does depend on any of ids, it's ok *)
+        vk
+      else
+        (* v depends on one of the cleared hyps:
+            we forget the computed value *)
+        dummy_lazy_val ()
+    in
+      remove_hyps ids check_context check_value hyps
+  in
+  (nhyps,terms)
+
+let clear_hyps_in_evi env evdref hyps concl ids =
+  match clear_hyps_in_evi_main env evdref hyps [concl] ids with
+  | (nhyps,[nconcl]) -> (nhyps,nconcl)
+  | _ -> assert false
+
+let clear_hyps2_in_evi env evdref hyps t concl ids =
+  match clear_hyps_in_evi_main env evdref hyps [t;concl] ids with
+  | (nhyps,[t;nconcl]) -> (nhyps,t,nconcl)
+  | _ -> assert false
+
+(* spiwack: a few functions to gather evars on which goals depend. *)
+let queue_set q is_dependent set =
+  Evar.Set.iter (fun a -> Queue.push (is_dependent,a) q) set
+let queue_term q is_dependent c =
+  queue_set q is_dependent (evars_of_term c)
+
+let process_dependent_evar q acc evm is_dependent e =
+  let evi = Evd.find evm e in
+  (* Queues evars appearing in the types of the goal (conclusion, then
+     hypotheses), they are all dependent. *)
+  queue_term q true evi.evar_concl;
+  List.iter begin fun decl ->
+    let open Context.Named.Declaration in
+    queue_term q true (get_type decl);
+    match decl with
+    | LocalAssum _ -> ()
+    | LocalDef (_,b,_) -> queue_term q true b
+  end (Environ.named_context_of_val evi.evar_hyps);
+  match evi.evar_body with
+  | Evar_empty ->
+      if is_dependent then Evar.Map.add e None acc else acc
+  | Evar_defined b ->
+      let subevars = evars_of_term b in
+      (* evars appearing in the definition of an evar [e] are marked
+         as dependent when [e] is dependent itself: if [e] is a
+         non-dependent goal, then, unless they are reach from another
+         path, these evars are just other non-dependent goals. *)
+      queue_set q is_dependent subevars;
+      if is_dependent then Evar.Map.add e (Some subevars) acc else acc
+
+let gather_dependent_evars q evm =
+  let acc = ref Evar.Map.empty in
+  while not (Queue.is_empty q) do
+    let (is_dependent,e) = Queue.pop q in
+    (* checks if [e] has already been added to [!acc] *)
+    begin if not (Evar.Map.mem e !acc) then
+        acc := process_dependent_evar q !acc evm is_dependent e  
+    end
+  done;
+  !acc
+
+let gather_dependent_evars evm l =
+  let q = Queue.create () in
+  List.iter (fun a -> Queue.add (false,a) q) l;
+  gather_dependent_evars q evm
+
+(* /spiwack *)
+
+(** The following functions return the set of undefined evars
+    contained in the object, the defined evars being traversed.
+    This is roughly a combination of the previous functions and
+    [nf_evar]. *)
+
+let undefined_evars_of_term evd t =
+  let rec evrec acc c =
+    match kind_of_term c with
+      | Evar (n, l) ->
+	let acc = Array.fold_left evrec acc l in
+	(try match (Evd.find evd n).evar_body with
+	  | Evar_empty -> Evar.Set.add n acc
+	  | Evar_defined c -> evrec acc c
+	 with Not_found -> anomaly ~label:"undefined_evars_of_term" (Pp.str "evar not found"))
+      | _ -> fold_constr evrec acc c
+  in
+  evrec Evar.Set.empty t
+
+let undefined_evars_of_named_context evd nc =
+  let open Context.Named.Declaration in
+  Context.Named.fold_outside
+    (fold (fun c s -> Evar.Set.union s (undefined_evars_of_term evd c)))
+    nc
+    ~init:Evar.Set.empty
+
+let undefined_evars_of_evar_info evd evi =
+  Evar.Set.union (undefined_evars_of_term evd evi.evar_concl)
+    (Evar.Set.union
+       (match evi.evar_body with
+	 | Evar_empty -> Evar.Set.empty
+	 | Evar_defined b -> undefined_evars_of_term evd b)
+       (undefined_evars_of_named_context evd
+	  (named_context_of_val evi.evar_hyps)))
+
+(* spiwack: this is a more complete version of
+   {!Termops.occur_evar}. The latter does not look recursively into an
+   [evar_map]. If unification only need to check superficially, tactics
+   do not have this luxury, and need the more complete version. *)
+let occur_evar_upto sigma n c =
+  let rec occur_rec c = match kind_of_term c with
+    | Evar (sp,_) when Evar.equal sp n -> raise Occur
+    | Evar e -> Option.iter occur_rec (existential_opt_value sigma e)
+    | _ -> iter_constr occur_rec c
+  in
+  try occur_rec c; false with Occur -> true
+
+(* We don't try to guess in which sort the type should be defined, since
+   any type has type Type. May cause some trouble, but not so far... *)
+
+let judge_of_new_Type evd =
+  let Sigma (s, evd', p) = Sigma.new_univ_variable univ_rigid evd in
+  Sigma ({ uj_val = mkSort (Type s); uj_type = mkSort (Type (Univ.super s)) }, evd', p)
+
+let subterm_source evk (loc,k) =
+  let evk = match k with
+    | Evar_kinds.SubEvar (evk) -> evk
+    | _ -> evk in
+  (loc,Evar_kinds.SubEvar evk)
+
+
+(** Term exploration up to instantiation. *)
+let kind_of_term_upto sigma t =
+  Constr.kind (whd_evar sigma t)
+
+(** [eq_constr_univs_test sigma1 sigma2 t u] tests equality of [t] and
+    [u] up to existential variable instantiation and equalisable
+    universes. The term [t] is interpreted in [sigma1] while [u] is
+    interpreted in [sigma2]. The universe constraints in [sigma2] are
+    assumed to be an extention of those in [sigma1]. *)
+let eq_constr_univs_test sigma1 sigma2 t u =
+  (* spiwack: mild code duplication with {!Evd.eq_constr_univs}. *)
+  let open Evd in
+  let fold cstr sigma =
+    try Some (add_universe_constraints sigma cstr)
+    with Univ.UniverseInconsistency _ | UniversesDiffer -> None
+  in
+  let ans =
+    Universes.eq_constr_univs_infer_with
+      (fun t -> kind_of_term_upto sigma1 t)
+      (fun u -> kind_of_term_upto sigma2 u)
+      (universes sigma2) fold t u sigma2
+  in
+  match ans with None -> false | Some _ -> true
+
+type type_constraint = types option
+type val_constraint = constr option
diff --git a/engine/evarutil.mli b/engine/evarutil.mli
new file mode 100644
index 000000000..ffff2c5dd
--- /dev/null
+++ b/engine/evarutil.mli
@@ -0,0 +1,221 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Term
+open Evd
+open Environ
+
+(** {5 This modules provides useful functions for unification modulo evars } *)
+
+(** {6 Metas} *)
+
+(** [new_meta] is a generator of unique meta variables *)
+val new_meta : unit -> metavariable
+val mk_new_meta : unit -> constr
+
+(** {6 Creating a fresh evar given their type and context} *)
+val new_evar :
+  env -> 'r Sigma.t -> ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t ->
+  ?candidates:constr list -> ?store:Store.t ->
+  ?naming:Misctypes.intro_pattern_naming_expr ->
+  ?principal:bool -> types -> (constr, 'r) Sigma.sigma
+
+val new_pure_evar :
+  named_context_val -> 'r Sigma.t -> ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t ->
+  ?candidates:constr list -> ?store:Store.t ->
+  ?naming:Misctypes.intro_pattern_naming_expr ->
+  ?principal:bool -> types -> (evar, 'r) Sigma.sigma
+
+val new_pure_evar_full : 'r Sigma.t -> evar_info -> (evar, 'r) Sigma.sigma
+
+(** the same with side-effects *)
+val e_new_evar :
+  env -> evar_map ref -> ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t ->
+  ?candidates:constr list -> ?store:Store.t ->
+  ?naming:Misctypes.intro_pattern_naming_expr ->
+  ?principal:bool -> types -> constr
+
+(** Create a new Type existential variable, as we keep track of 
+    them during type-checking and unification. *)
+val new_type_evar :
+  env -> 'r Sigma.t -> ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t ->
+  ?naming:Misctypes.intro_pattern_naming_expr -> ?principal:bool -> rigid ->
+  (constr * sorts, 'r) Sigma.sigma
+
+val e_new_type_evar : env -> evar_map ref ->
+  ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t ->
+  ?naming:Misctypes.intro_pattern_naming_expr -> ?principal:bool -> rigid -> constr * sorts
+
+val new_Type : ?rigid:rigid -> env -> 'r Sigma.t -> (constr, 'r) Sigma.sigma
+val e_new_Type : ?rigid:rigid -> env -> evar_map ref -> constr
+
+val restrict_evar : 'r Sigma.t -> existential_key -> Filter.t ->
+  constr list option -> (existential_key, 'r) Sigma.sigma
+
+(** Polymorphic constants *)
+
+val new_global : 'r Sigma.t -> Globnames.global_reference -> (constr, 'r) Sigma.sigma
+val e_new_global : evar_map ref -> Globnames.global_reference -> constr
+
+(** Create a fresh evar in a context different from its definition context:
+   [new_evar_instance sign evd ty inst] creates a new evar of context
+   [sign] and type [ty], [inst] is a mapping of the evar context to
+   the context where the evar should occur. This means that the terms
+   of [inst] are typed in the occurrence context and their type (seen
+   as a telescope) is [sign] *)
+val new_evar_instance :
+ named_context_val -> 'r Sigma.t -> types -> 
+  ?src:Loc.t * Evar_kinds.t -> ?filter:Filter.t -> ?candidates:constr list ->
+  ?store:Store.t -> ?naming:Misctypes.intro_pattern_naming_expr ->
+  ?principal:bool ->
+  constr list -> (constr, 'r) Sigma.sigma
+
+val make_pure_subst : evar_info -> constr array -> (Id.t * constr) list
+
+val safe_evar_value : evar_map -> existential -> constr option
+
+(** {6 Evars/Metas switching...} *)
+
+val non_instantiated : evar_map -> evar_info Evar.Map.t
+
+(** {6 Unification utils} *)
+
+(** [head_evar c] returns the head evar of [c] if any *)
+exception NoHeadEvar
+val head_evar : constr -> existential_key (** may raise NoHeadEvar *)
+
+(* Expand head evar if any *)
+val whd_head_evar :  evar_map -> constr -> constr
+
+(* An over-approximation of [has_undefined (nf_evars evd c)] *)
+val has_undefined_evars : evar_map -> constr -> bool
+
+val is_ground_term :  evar_map -> constr -> bool
+val is_ground_env  :  evar_map -> env -> bool
+
+(** [gather_dependent_evars evm seeds] classifies the evars in [evm]
+    as dependent_evars and goals (these may overlap). A goal is an
+    evar in [seeds] or an evar appearing in the (partial) definition
+    of a goal. A dependent evar is an evar appearing in the type
+    (hypotheses and conclusion) of a goal, or in the type or (partial)
+    definition of a dependent evar.  The value return is a map
+    associating to each dependent evar [None] if it has no (partial)
+    definition or [Some s] if [s] is the list of evars appearing in
+    its (partial) definition. *)
+val gather_dependent_evars : evar_map -> evar list -> (Evar.Set.t option) Evar.Map.t
+
+(** The following functions return the set of undefined evars
+    contained in the object, the defined evars being traversed.
+    This is roughly a combination of the previous functions and
+    [nf_evar]. *)
+
+val undefined_evars_of_term : evar_map -> constr -> Evar.Set.t
+val undefined_evars_of_named_context : evar_map -> Context.Named.t -> Evar.Set.t
+val undefined_evars_of_evar_info : evar_map -> evar_info -> Evar.Set.t
+
+(** [occur_evar_upto sigma k c] returns [true] if [k] appears in
+    [c]. It looks up recursively in [sigma] for the value of existential
+    variables. *)
+val occur_evar_upto : evar_map -> Evar.t -> Constr.t -> bool
+
+(** {6 Value/Type constraints} *)
+
+val judge_of_new_Type : 'r Sigma.t -> (unsafe_judgment, 'r) Sigma.sigma
+
+(***********************************************************)
+
+(** [flush_and_check_evars] raise [Uninstantiated_evar] if an evar remains
+    uninstantiated; [nf_evar] leaves uninstantiated evars as is *)
+
+val whd_evar :  evar_map -> constr -> constr
+val nf_evar :  evar_map -> constr -> constr
+val j_nf_evar :  evar_map -> unsafe_judgment -> unsafe_judgment
+val jl_nf_evar :
+   evar_map -> unsafe_judgment list -> unsafe_judgment list
+val jv_nf_evar :
+   evar_map -> unsafe_judgment array -> unsafe_judgment array
+val tj_nf_evar :
+   evar_map -> unsafe_type_judgment -> unsafe_type_judgment
+
+val nf_named_context_evar : evar_map -> Context.Named.t -> Context.Named.t
+val nf_rel_context_evar : evar_map -> Context.Rel.t -> Context.Rel.t
+val nf_env_evar : evar_map -> env -> env
+
+val nf_evar_info : evar_map -> evar_info -> evar_info
+val nf_evar_map : evar_map -> evar_map
+val nf_evar_map_undefined : evar_map -> evar_map
+
+(** Presenting terms without solved evars *)
+
+val nf_evars_universes : evar_map -> constr -> constr
+
+val nf_evars_and_universes : evar_map -> evar_map * (constr -> constr)
+val e_nf_evars_and_universes : evar_map ref -> (constr -> constr) * Universes.universe_opt_subst
+
+(** Normalize the evar map w.r.t. universes, after simplification of constraints.
+    Return the substitution function for constrs as well. *)
+val nf_evar_map_universes : evar_map -> evar_map * (constr -> constr)
+
+(** Replacing all evars, possibly raising [Uninstantiated_evar] *)
+exception Uninstantiated_evar of existential_key
+val flush_and_check_evars :  evar_map -> constr -> constr
+
+(** {6 Term manipulation up to instantiation} *)
+
+(** Like {!Constr.kind} except that [kind_of_term sigma t] exposes [t]
+    as an evar [e] only if [e] is uninstantiated in [sigma]. Otherwise the
+    value of [e] in [sigma] is (recursively) used. *)
+val kind_of_term_upto : evar_map -> constr -> (constr,types) kind_of_term
+
+(** [eq_constr_univs_test sigma1 sigma2 t u] tests equality of [t] and
+    [u] up to existential variable instantiation and equalisable
+    universes. The term [t] is interpreted in [sigma1] while [u] is
+    interpreted in [sigma2]. The universe constraints in [sigma2] are
+    assumed to be an extention of those in [sigma1]. *)
+val eq_constr_univs_test : evar_map -> evar_map -> constr -> constr -> bool
+
+(** {6 Removing hyps in evars'context}
+raise OccurHypInSimpleClause if the removal breaks dependencies *)
+
+type clear_dependency_error =
+| OccurHypInSimpleClause of Id.t option
+| EvarTypingBreak of existential
+
+exception ClearDependencyError of Id.t * clear_dependency_error
+
+(* spiwack: marks an evar that has been "defined" by clear.
+    used by [Goal] and (indirectly) [Proofview] to handle the clear tactic gracefully*)
+val cleared : bool Store.field
+
+val clear_hyps_in_evi : env -> evar_map ref -> named_context_val -> types ->
+  Id.Set.t -> named_context_val * types
+
+val clear_hyps2_in_evi : env -> evar_map ref -> named_context_val -> types -> types ->
+  Id.Set.t -> named_context_val * types * types
+
+val push_rel_context_to_named_context : Environ.env -> types ->
+  named_context_val * types * constr list * constr list * (identifier*constr) list
+
+val generalize_evar_over_rels : evar_map -> existential -> types * constr list
+
+(** Evar combinators *)
+
+val evd_comb0 : (evar_map -> evar_map * 'a) -> evar_map ref -> 'a
+val evd_comb1 : (evar_map -> 'b -> evar_map * 'a) -> evar_map ref -> 'b -> 'a
+val evd_comb2 : (evar_map -> 'b -> 'c -> evar_map * 'a) -> evar_map ref -> 'b -> 'c -> 'a
+
+val subterm_source : existential_key -> Evar_kinds.t Loc.located ->
+  Evar_kinds.t Loc.located
+
+val meta_counter_summary_name : string
+
+(** Deprecater *)
+
+type type_constraint = types option
+type val_constraint = constr option
diff --git a/engine/proofview.ml b/engine/proofview.ml
new file mode 100644
index 000000000..ba664cafa
--- /dev/null
+++ b/engine/proofview.ml
@@ -0,0 +1,1211 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+
+(** This files defines the basic mechanism of proofs: the [proofview]
+    type is the state which tactics manipulate (a global state for
+    existential variables, together with the list of goals), and the type
+    ['a tactic] is the (abstract) type of tactics modifying the proof
+    state and returning a value of type ['a]. *)
+
+open Pp
+open Util
+open Proofview_monad
+open Sigma.Notations
+open Context.Named.Declaration
+
+(** Main state of tactics *)
+type proofview = Proofview_monad.proofview
+
+type entry = (Term.constr * Term.types) list
+
+(** Returns a stylised view of a proofview for use by, for instance,
+    ide-s. *)
+(* spiwack: the type of [proofview] will change as we push more
+   refined functions to ide-s. This would be better than spawning a
+   new nearly identical function everytime. Hence the generic name. *)
+(* In this version: returns the list of focused goals together with
+   the [evar_map] context. *)
+let proofview p =
+  p.comb , p.solution
+
+let compact el ({ solution } as pv) =
+  let nf = Evarutil.nf_evar solution in
+  let size = Evd.fold (fun _ _ i -> i+1) solution 0 in
+  let new_el = List.map (fun (t,ty) -> nf t, nf ty) el in
+  let pruned_solution = Evd.drop_all_defined solution in
+  let apply_subst_einfo _ ei =
+    Evd.({ ei with
+       evar_concl =  nf ei.evar_concl;
+       evar_hyps = Environ.map_named_val nf ei.evar_hyps;
+       evar_candidates = Option.map (List.map nf) ei.evar_candidates }) in
+  let new_solution = Evd.raw_map_undefined apply_subst_einfo pruned_solution in
+  let new_size = Evd.fold (fun _ _ i -> i+1) new_solution 0 in
+  msg_info (Pp.str (Printf.sprintf "Evars: %d -> %d\n" size new_size));
+  new_el, { pv with solution = new_solution; }
+
+
+(** {6 Starting and querying a proof view} *)
+
+type telescope =
+  | TNil of Evd.evar_map
+  | TCons of Environ.env * Evd.evar_map * Term.types * (Evd.evar_map -> Term.constr -> telescope)
+
+let typeclass_resolvable = Evd.Store.field ()
+
+let dependent_init =
+  (* Goals are created with a store which marks them as unresolvable
+     for type classes. *)
+  let store = Evd.Store.set Evd.Store.empty typeclass_resolvable () in
+  (* Goals don't have a source location. *)
+  let src = (Loc.ghost,Evar_kinds.GoalEvar) in
+  (* Main routine *)
+  let rec aux = function
+  | TNil sigma -> [], { solution = sigma; comb = []; shelf = [] }
+  | TCons (env, sigma, typ, t) ->
+    let sigma = Sigma.Unsafe.of_evar_map sigma in
+    let Sigma (econstr, sigma, _) = Evarutil.new_evar env sigma ~src ~store typ in
+    let sigma = Sigma.to_evar_map sigma in
+    let ret, { solution = sol; comb = comb } = aux (t sigma econstr) in
+    let (gl, _) = Term.destEvar econstr in
+    let entry = (econstr, typ) :: ret in
+    entry, { solution = sol; comb = gl :: comb; shelf = [] }
+  in
+  fun t ->
+    let entry, v = aux t in
+    (* The created goal are not to be shelved. *)
+    let solution = Evd.reset_future_goals v.solution in
+    entry, { v with solution }
+
+let init =
+  let rec aux sigma = function
+    | [] -> TNil sigma
+    | (env,g)::l -> TCons (env,sigma,g,(fun sigma _ -> aux sigma l))
+  in
+  fun sigma l -> dependent_init (aux sigma l)
+
+let initial_goals initial = initial
+
+let finished = function
+  | {comb = []} -> true
+  | _  -> false
+
+let return { solution=defs } = defs
+
+let return_constr { solution = defs } c = Evarutil.nf_evar defs c
+
+let partial_proof entry pv = CList.map (return_constr pv) (CList.map fst entry)
+
+
+(** {6 Focusing commands} *)
+
+(** A [focus_context] represents the part of the proof view which has
+    been removed by a focusing action, it can be used to unfocus later
+    on. *)
+(* First component is a reverse list of the goals which come before
+   and second component is the list of the goals which go after (in
+   the expected order). *)
+type focus_context = Evar.t list * Evar.t list
+
+
+(** Returns a stylised view of a focus_context for use by, for
+    instance, ide-s. *)
+(* spiwack: the type of [focus_context] will change as we push more
+   refined functions to ide-s. This would be better than spawning a
+   new nearly identical function everytime. Hence the generic name. *)
+(* In this version: the goals in the context, as a "zipper" (the first
+   list is in reversed order). *)
+let focus_context f = f
+
+(** This (internal) function extracts a sublist between two indices,
+    and returns this sublist together with its context: if it returns
+    [(a,(b,c))] then [a] is the sublist and (rev b)@a@c is the
+    original list.  The focused list has lenght [j-i-1] and contains
+    the goals from number [i] to number [j] (both included) the first
+    goal of the list being numbered [1].  [focus_sublist i j l] raises
+    [IndexOutOfRange] if [i > length l], or [j > length l] or [j <
+    i]. *)
+let focus_sublist i j l =
+  let (left,sub_right) = CList.goto (i-1) l in
+  let (sub, right) = 
+    try CList.chop (j-i+1) sub_right
+    with Failure _ -> raise CList.IndexOutOfRange
+  in
+  (sub, (left,right))
+
+(** Inverse operation to the previous one. *)
+let unfocus_sublist (left,right) s =
+  CList.rev_append left (s@right)
+
+
+(** [focus i j] focuses a proofview on the goals from index [i] to
+    index [j] (inclusive, goals are indexed from [1]). I.e. goals
+    number [i] to [j] become the only focused goals of the returned
+    proofview.  It returns the focused proofview, and a context for
+    the focus stack. *)
+let focus i j sp =
+  let (new_comb, context) = focus_sublist i j sp.comb in
+  ( { sp with comb = new_comb } , context )
+
+
+(** [advance sigma g] returns [Some g'] if [g'] is undefined and is
+    the current avatar of [g] (for instance [g] was changed by [clear]
+    into [g']). It returns [None] if [g] has been (partially)
+    solved. *)
+(* spiwack: [advance] is probably performance critical, and the good
+   behaviour of its definition may depend sensitively to the actual
+   definition of [Evd.find]. Currently, [Evd.find] starts looking for
+   a value in the heap of undefined variable, which is small. Hence in
+   the most common case, where [advance] is applied to an unsolved
+   goal ([advance] is used to figure if a side effect has modified the
+   goal) it terminates quickly. *)
+let rec advance sigma g =
+  let open Evd in
+  let evi = Evd.find sigma g in
+  match evi.evar_body with
+  | Evar_empty -> Some g
+  | Evar_defined v ->
+      if Option.default false (Store.get evi.evar_extra Evarutil.cleared) then
+        let (e,_) = Term.destEvar v in
+        advance sigma e
+      else
+        None
+
+(** [undefined defs l] is the list of goals in [l] which are still
+    unsolved (after advancing cleared goals). *)
+let undefined defs l = CList.map_filter (advance defs) l
+
+(** Unfocuses a proofview with respect to a context. *)
+let unfocus c sp =
+  { sp with comb = undefined sp.solution (unfocus_sublist c sp.comb) }
+
+
+(** {6 The tactic monad} *)
+
+(** - Tactics are objects which apply a transformation to all the
+    subgoals of the current view at the same time. By opposition to
+    the old vision of applying it to a single goal. It allows tactics
+    such as [shelve_unifiable], tactics to reorder the focused goals,
+    or global automation tactic for dependent subgoals (instantiating
+    an evar has influences on the other goals of the proof in
+    progress, not being able to take that into account causes the
+    current eauto tactic to fail on some instances where it could
+    succeed).  Another benefit is that it is possible to write tactics
+    that can be executed even if there are no focused goals.
+    - Tactics form a monad ['a tactic], in a sense a tactic can be
+    seen as a function (without argument) which returns a value of
+    type 'a and modifies the environment (in our case: the view).
+    Tactics of course have arguments, but these are given at the
+    meta-level as OCaml functions.  Most tactics in the sense we are
+    used to return [()], that is no really interesting values. But
+    some might pass information around.  The tactics seen in Coq's
+    Ltac are (for now at least) only [unit tactic], the return values
+    are kept for the OCaml toolkit.  The operation or the monad are
+    [Proofview.tclUNIT] (which is the "return" of the tactic monad)
+    [Proofview.tclBIND] (which is the "bind") and [Proofview.tclTHEN]
+    (which is a specialized bind on unit-returning tactics).
+    - Tactics have support for full-backtracking. Tactics can be seen
+    having multiple success: if after returning the first success a
+    failure is encountered, the tactic can backtrack and use a second
+    success if available. The state is backtracked to its previous
+    value, except the non-logical state defined in the {!NonLogical}
+    module below.
+*)
+(* spiwack: as far as I'm aware this doesn't really relate to
+   F. Kirchner and C. Muñoz. *)
+
+module Proof = Logical
+
+(** type of tactics:
+
+   tactics can
+   - access the environment,
+   - report unsafe status, shelved goals and given up goals
+   - access and change the current [proofview]
+   - backtrack on previous changes of the proofview *)
+type +'a tactic = 'a Proof.t
+
+(** Applies a tactic to the current proofview. *)
+let apply env t sp =
+  let open Logic_monad in
+  let ans = Proof.repr (Proof.run t false (sp,env)) in
+  let ans = Logic_monad.NonLogical.run ans in
+  match ans with
+  | Nil (e, info) -> iraise (TacticFailure e, info)
+  | Cons ((r, (state, _), status, info), _) ->
+    let (status, gaveup) = status in
+    let status = (status, state.shelf, gaveup) in
+    let state = { state with shelf = [] } in
+    r, state, status, Trace.to_tree info
+
+
+
+(** {7 Monadic primitives} *)
+
+(** Unit of the tactic monad. *)
+let tclUNIT = Proof.return
+
+(** Bind operation of the tactic monad. *)
+let tclBIND = Proof.(>>=)
+
+(** Interpretes the ";" (semicolon) of Ltac. As a monadic operation,
+    it's a specialized "bind". *)
+let tclTHEN = Proof.(>>)
+
+(** [tclIGNORE t] has the same operational content as [t], but drops
+    the returned value. *)
+let tclIGNORE = Proof.ignore
+
+module Monad = Proof
+
+
+
+(** {7 Failure and backtracking} *)
+
+
+(** [tclZERO e] fails with exception [e]. It has no success. *)
+let tclZERO ?info e =
+  let info = match info with
+  | None -> Exninfo.null
+  | Some info -> info
+  in
+  Proof.zero (e, info)
+
+(** [tclOR t1 t2] behaves like [t1] as long as [t1] succeeds. Whenever
+    the successes of [t1] have been depleted and it failed with [e],
+    then it behaves as [t2 e]. In other words, [tclOR] inserts a
+    backtracking point. *)
+let tclOR = Proof.plus
+
+(** [tclORELSE t1 t2] is equal to [t1] if [t1] has at least one
+    success or [t2 e] if [t1] fails with [e]. It is analogous to
+    [try/with] handler of exception in that it is not a backtracking
+    point. *)
+let tclORELSE t1 t2 =
+  let open Logic_monad in
+  let open Proof in
+  split t1 >>= function
+    | Nil e -> t2 e
+    | Cons (a,t1') -> plus (return a) t1'
+
+(** [tclIFCATCH a s f] is a generalisation of {!tclORELSE}: if [a]
+    succeeds at least once then it behaves as [tclBIND a s] otherwise,
+    if [a] fails with [e], then it behaves as [f e]. *)
+let tclIFCATCH a s f =
+  let open Logic_monad in
+  let open Proof in
+  split a >>= function
+    | Nil e -> f e
+    | Cons (x,a') -> plus (s x) (fun e -> (a' e) >>= fun x' -> (s x'))
+
+(** [tclONCE t] behave like [t] except it has at most one success:
+    [tclONCE t] stops after the first success of [t]. If [t] fails
+    with [e], [tclONCE t] also fails with [e]. *)
+let tclONCE = Proof.once
+
+exception MoreThanOneSuccess
+let _ = Errors.register_handler begin function
+  | MoreThanOneSuccess -> Errors.error "This tactic has more than one success."
+  | _ -> raise Errors.Unhandled
+end
+
+(** [tclEXACTLY_ONCE e t] succeeds as [t] if [t] has exactly one
+    success. Otherwise it fails. The tactic [t] is run until its first
+    success, then a failure with exception [e] is simulated. It [t]
+    yields another success, then [tclEXACTLY_ONCE e t] fails with
+    [MoreThanOneSuccess] (it is a user error). Otherwise,
+    [tclEXACTLY_ONCE e t] succeeds with the first success of
+    [t]. Notice that the choice of [e] is relevant, as the presence of
+    further successes may depend on [e] (see {!tclOR}). *)
+let tclEXACTLY_ONCE e t =
+  let open Logic_monad in
+  let open Proof in
+  split t >>= function
+    | Nil (e, info) -> tclZERO ~info e
+    | Cons (x,k) ->
+        Proof.split (k (e, Exninfo.null)) >>= function
+          | Nil _ -> tclUNIT x
+          | _ -> tclZERO MoreThanOneSuccess
+
+
+(** [tclCASE t] wraps the {!Proofview_monad.Logical.split} primitive. *)
+type 'a case =
+| Fail of iexn
+| Next of 'a * (iexn -> 'a tactic)
+let tclCASE t =
+  let open Logic_monad in
+  let map = function
+  | Nil e -> Fail e
+  | Cons (x, t) -> Next (x, t)
+  in
+  Proof.map map (Proof.split t)
+
+let tclBREAK = Proof.break
+
+
+
+(** {7 Focusing tactics} *)
+
+exception NoSuchGoals of int
+
+(* This hook returns a string to be appended to the usual message.
+   Primarily used to add a suggestion about the right bullet to use to
+   focus the next goal, if applicable. *)
+let nosuchgoals_hook:(int -> std_ppcmds) ref = ref (fun n -> mt ())
+let set_nosuchgoals_hook f = nosuchgoals_hook := f
+
+
+
+(* This uses the hook above *)
+let _ = Errors.register_handler begin function
+  | NoSuchGoals n ->
+    let suffix = !nosuchgoals_hook n in
+    Errors.errorlabstrm ""
+      (str "No such " ++ str (String.plural n "goal") ++ str "." ++ suffix)
+  | _ -> raise Errors.Unhandled
+end
+
+(** [tclFOCUS_gen nosuchgoal i j t] applies [t] in a context where
+    only the goals numbered [i] to [j] are focused (the rest of the goals
+    is restored at the end of the tactic). If the range [i]-[j] is not
+    valid, then it [tclFOCUS_gen nosuchgoal i j t] is [nosuchgoal]. *)
+let tclFOCUS_gen nosuchgoal i j t =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  try
+    let (focused,context) = focus i j initial in
+    Pv.set focused >>
+    t >>= fun result ->
+    Pv.modify (fun next -> unfocus context next) >>
+    return result
+  with CList.IndexOutOfRange -> nosuchgoal
+
+let tclFOCUS i j t = tclFOCUS_gen (tclZERO (NoSuchGoals (j+1-i))) i j t
+let tclTRYFOCUS i j t = tclFOCUS_gen (tclUNIT ()) i j t
+
+(** Like {!tclFOCUS} but selects a single goal by name. *)
+let tclFOCUSID id t =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  try
+    let ev = Evd.evar_key id initial.solution in
+    try
+      let n = CList.index Evar.equal ev initial.comb in
+      (* goal is already under focus *)
+      let (focused,context) = focus n n initial in
+      Pv.set focused >>
+        t >>= fun result ->
+      Pv.modify (fun next -> unfocus context next) >>
+        return result
+    with Not_found ->
+      (* otherwise, save current focus and work purely on the shelve *)
+      Comb.set [ev] >>
+        t >>= fun result ->
+      Comb.set initial.comb  >>
+        return result
+  with Not_found -> tclZERO (NoSuchGoals 1)
+
+(** {7 Dispatching on goals} *)
+
+exception SizeMismatch of int*int
+let _ = Errors.register_handler begin function
+  | SizeMismatch (i,_) ->
+      let open Pp in
+      let errmsg =
+        str"Incorrect number of goals" ++ spc() ++
+        str"(expected "++int i++str(String.plural i " tactic") ++ str")."
+      in
+      Errors.errorlabstrm "" errmsg
+  | _ -> raise Errors.Unhandled
+end
+
+(** A variant of [Monad.List.iter] where we iter over the focused list
+    of goals. The argument tactic is executed in a focus comprising
+    only of the current goal, a goal which has been solved by side
+    effect is skipped. The generated subgoals are concatenated in
+    order.  *)
+let iter_goal i =
+  let open Proof in
+  Comb.get >>= fun initial ->
+  Proof.List.fold_left begin fun (subgoals as cur) goal ->
+    Solution.get >>= fun step ->
+    match advance step goal with
+    | None -> return cur
+    | Some goal ->
+        Comb.set [goal] >>
+        i goal >>
+        Proof.map (fun comb -> comb :: subgoals) Comb.get
+  end [] initial >>= fun subgoals ->
+  Solution.get >>= fun evd ->
+  Comb.set CList.(undefined evd (flatten (rev subgoals)))
+
+(** A variant of [Monad.List.fold_left2] where the first list is the
+    list of focused goals. The argument tactic is executed in a focus
+    comprising only of the current goal, a goal which has been solved
+    by side effect is skipped. The generated subgoals are concatenated
+    in order. *)
+let fold_left2_goal i s l =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  let err =
+    return () >>= fun () -> (* Delay the computation of list lengths. *)
+    tclZERO (SizeMismatch (CList.length initial.comb,CList.length l))
+  in 
+  Proof.List.fold_left2 err begin fun ((r,subgoals) as cur) goal a ->
+    Solution.get >>= fun step ->
+    match advance step goal with
+    | None -> return cur
+    | Some goal ->
+        Comb.set [goal] >>
+        i goal a r >>= fun r ->
+        Proof.map (fun comb -> (r, comb :: subgoals)) Comb.get
+  end (s,[]) initial.comb l >>= fun (r,subgoals) ->
+  Solution.get >>= fun evd ->
+  Comb.set CList.(undefined evd (flatten (rev subgoals))) >>
+  return r
+
+(** Dispatch tacticals are used to apply a different tactic to each
+    goal under focus. They come in two flavours: [tclDISPATCH] takes a
+    list of [unit tactic]-s and build a [unit tactic]. [tclDISPATCHL]
+    takes a list of ['a tactic] and returns an ['a list tactic].
+
+    They both work by applying each of the tactic in a focus
+    restricted to the corresponding goal (starting with the first
+    goal). In the case of [tclDISPATCHL], the tactic returns a list of
+    the same size as the argument list (of tactics), each element
+    being the result of the tactic executed in the corresponding goal.
+
+    When the length of the tactic list is not the number of goal,
+    raises [SizeMismatch (g,t)] where [g] is the number of available
+    goals, and [t] the number of tactics passed.
+
+    [tclDISPATCHGEN join tacs] generalises both functions as the
+    successive results of [tacs] are stored in reverse order in a
+    list, and [join] is used to convert the result into the expected
+    form. *)
+let tclDISPATCHGEN0 join tacs =
+  match tacs with
+  | [] ->
+      begin 
+        let open Proof in
+        Comb.get >>= function
+        | [] -> tclUNIT (join [])
+        | comb -> tclZERO (SizeMismatch (CList.length comb,0))
+      end
+  | [tac] ->
+      begin
+        let open Proof in
+        Pv.get >>= function
+        | { comb=[goal] ; solution } ->
+            begin match advance solution goal with
+            | None -> tclUNIT (join [])
+            | Some _ -> Proof.map (fun res -> join [res]) tac
+            end
+        | {comb} -> tclZERO (SizeMismatch(CList.length comb,1))
+      end
+  | _ ->
+      let iter _ t cur = Proof.map (fun y -> y :: cur) t in
+      let ans = fold_left2_goal iter [] tacs in
+      Proof.map join ans
+
+let tclDISPATCHGEN join tacs =
+  let branch t = InfoL.tag (Info.DBranch) t in
+  let tacs = CList.map branch tacs in
+  InfoL.tag (Info.Dispatch) (tclDISPATCHGEN0 join tacs)
+
+let tclDISPATCH tacs = tclDISPATCHGEN Pervasives.ignore tacs
+
+let tclDISPATCHL tacs = tclDISPATCHGEN CList.rev tacs
+
+
+(** [extend_to_list startxs rx endxs l] builds a list
+    [startxs@[rx,...,rx]@endxs] of the same length as [l]. Raises
+    [SizeMismatch] if [startxs@endxs] is already longer than [l]. *)
+let extend_to_list startxs rx endxs l =
+  (* spiwack: I use [l] essentially as a natural number *)
+  let rec duplicate acc = function
+    | [] -> acc
+    | _::rest -> duplicate (rx::acc) rest
+  in
+  let rec tail to_match rest =
+    match rest, to_match with
+    | [] , _::_ -> raise (SizeMismatch(0,0)) (* placeholder *)
+    | _::rest , _::to_match -> tail to_match rest
+    | _ , [] -> duplicate endxs rest
+  in
+  let rec copy pref rest =
+    match rest,pref with
+    | [] , _::_ -> raise (SizeMismatch(0,0)) (* placeholder *)
+    | _::rest, a::pref -> a::(copy pref rest)
+    | _ , [] -> tail endxs rest
+  in
+  copy startxs l
+
+(** [tclEXTEND b r e] is a variant of {!tclDISPATCH}, where the [r]
+    tactic is "repeated" enough time such that every goal has a tactic
+    assigned to it ([b] is the list of tactics applied to the first
+    goals, [e] to the last goals, and [r] is applied to every goal in
+    between). *)
+let tclEXTEND tacs1 rtac tacs2 =
+  let open Proof in
+  Comb.get >>= fun comb ->
+  try
+    let tacs = extend_to_list tacs1 rtac tacs2 comb in
+    tclDISPATCH tacs
+  with SizeMismatch _ ->
+    tclZERO (SizeMismatch(
+      CList.length comb,
+      (CList.length tacs1)+(CList.length tacs2)))
+(* spiwack: failure occurs only when the number of goals is too
+   small. Hence we can assume that [rtac] is replicated 0 times for
+   any error message. *)
+
+(** [tclEXTEND [] tac []]. *)
+let tclINDEPENDENT tac =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  match initial.comb with
+  | [] -> tclUNIT ()
+  | [_] -> tac
+  | _ ->
+      let tac = InfoL.tag (Info.DBranch) tac in
+      InfoL.tag (Info.Dispatch) (iter_goal (fun _ -> tac))
+
+
+
+(** {7 Goal manipulation} *)
+
+(** Shelves all the goals under focus. *)
+let shelve =
+  let open Proof in
+  Comb.get >>= fun initial ->
+  Comb.set [] >>
+  InfoL.leaf (Info.Tactic (fun () -> Pp.str"shelve")) >>
+  Shelf.modify (fun gls -> gls @ initial)
+
+
+(** [contained_in_info e evi] checks whether the evar [e] appears in
+    the hypotheses, the conclusion or the body of the evar_info
+    [evi]. Note: since we want to use it on goals, the body is actually
+    supposed to be empty. *)
+let contained_in_info sigma e evi =
+  Evar.Set.mem e (Evd.evars_of_filtered_evar_info (Evarutil.nf_evar_info sigma evi))
+
+(** [depends_on sigma src tgt] checks whether the goal [src] appears
+    as an existential variable in the definition of the goal [tgt] in
+    [sigma]. *)
+let depends_on sigma src tgt =
+  let evi = Evd.find sigma tgt in
+  contained_in_info sigma src evi
+
+(** [unifiable sigma g l] checks whether [g] appears in another
+    subgoal of [l]. The list [l] may contain [g], but it does not
+    affect the result. *)
+let unifiable sigma g l =
+  CList.exists (fun tgt -> not (Evar.equal g tgt) && depends_on sigma g tgt) l
+
+(** [partition_unifiable sigma l] partitions [l] into a pair [(u,n)]
+    where [u] is composed of the unifiable goals, i.e. the goals on
+    whose definition other goals of [l] depend, and [n] are the
+    non-unifiable goals. *)
+let partition_unifiable sigma l =
+  CList.partition (fun g -> unifiable sigma g l) l
+
+(** Shelves the unifiable goals under focus, i.e. the goals which
+    appear in other goals under focus (the unfocused goals are not
+    considered). *)
+let shelve_unifiable =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  let (u,n) = partition_unifiable initial.solution initial.comb in
+  Comb.set n >>
+  InfoL.leaf (Info.Tactic (fun () -> Pp.str"shelve_unifiable")) >>
+  Shelf.modify (fun gls -> gls @ u)
+
+(** [guard_no_unifiable] returns the list of unifiable goals if some
+    goals are unifiable (see {!shelve_unifiable}) in the current focus. *)
+let guard_no_unifiable =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  let (u,n) = partition_unifiable initial.solution initial.comb in
+  match u with
+  | [] -> tclUNIT None
+  | gls ->
+      let l = CList.map (fun g -> Evd.dependent_evar_ident g initial.solution) gls in
+      let l = CList.map (fun id -> Names.Name id) l in
+      tclUNIT (Some l)
+
+(** [unshelve l p] adds all the goals in [l] at the end of the focused
+    goals of p *)
+let unshelve l p =
+  (* advance the goals in case of clear *)
+  let l = undefined p.solution l in
+  { p with comb = p.comb@l }
+
+let with_shelf tac =
+  let open Proof in
+  Pv.get >>= fun pv ->
+  let { shelf; solution } = pv in
+  Pv.set { pv with shelf = []; solution = Evd.reset_future_goals solution } >>
+  tac >>= fun ans ->
+  Pv.get >>= fun npv ->
+  let { shelf = gls; solution = sigma } = npv in
+  let gls' = Evd.future_goals sigma in
+  let fgoals = Evd.future_goals solution in
+  let pgoal = Evd.principal_future_goal solution in
+  let sigma = Evd.restore_future_goals sigma fgoals pgoal in
+  Pv.set { npv with shelf; solution = sigma } >>
+  tclUNIT (CList.rev_append gls' gls, ans)
+
+(** [goodmod p m] computes the representative of [p] modulo [m] in the
+    interval [[0,m-1]].*)
+let goodmod p m =
+  let p' = p mod m in
+  (* if [n] is negative [n mod l] is negative of absolute value less
+     than [l], so [(n mod l)+l] is the representative of [n] in the
+     interval [[0,l-1]].*)
+  if p' < 0 then p'+m else p'
+
+let cycle n =
+  let open Proof in
+  InfoL.leaf (Info.Tactic (fun () -> Pp.(str"cycle "++int n))) >>
+  Comb.modify begin fun initial ->
+    let l = CList.length initial in
+    let n' = goodmod n l in
+    let (front,rear) = CList.chop n' initial in
+    rear@front
+  end
+
+let swap i j =
+  let open Proof in
+  InfoL.leaf (Info.Tactic (fun () -> Pp.(hov 2 (str"swap"++spc()++int i++spc()++int j)))) >>
+  Comb.modify begin fun initial ->
+    let l = CList.length initial in
+    let i = if i>0 then i-1 else i and j = if j>0 then j-1 else j in
+    let i = goodmod i l and j = goodmod j l in
+    CList.map_i begin fun k x ->
+      match k with
+      | k when Int.equal k i -> CList.nth initial j
+      | k when Int.equal k j -> CList.nth initial i
+      | _ -> x
+    end 0 initial
+  end
+
+let revgoals =
+  let open Proof in
+  InfoL.leaf (Info.Tactic (fun () -> Pp.str"revgoals")) >>
+  Comb.modify CList.rev
+
+let numgoals =
+  let open Proof in
+  Comb.get >>= fun comb ->
+  return (CList.length comb)
+
+
+
+(** {7 Access primitives} *)
+
+let tclEVARMAP = Solution.get
+
+let tclENV = Env.get
+
+
+
+(** {7 Put-like primitives} *)
+
+
+let emit_side_effects eff x =
+  { x with solution = Evd.emit_side_effects eff x.solution }
+
+let tclEFFECTS eff =
+  let open Proof in
+  return () >>= fun () -> (* The Global.env should be taken at exec time *)
+  Env.set (Global.env ()) >>
+  Pv.modify (fun initial -> emit_side_effects eff initial)
+
+let mark_as_unsafe = Status.put false
+
+(** Gives up on the goal under focus. Reports an unsafe status. Proofs
+    with given up goals cannot be closed. *)
+let give_up =
+  let open Proof in
+  Comb.get >>= fun initial ->
+  Comb.set [] >>
+  mark_as_unsafe >>
+  InfoL.leaf (Info.Tactic (fun () -> Pp.str"give_up")) >>
+  Giveup.put initial
+
+
+
+(** {7 Control primitives} *)
+
+
+module Progress = struct
+
+  let eq_constr = Evarutil.eq_constr_univs_test
+
+  (** equality function on hypothesis contexts *)
+  let eq_named_context_val sigma1 sigma2 ctx1 ctx2 =
+    let open Environ in
+    let c1 = named_context_of_val ctx1 and c2 = named_context_of_val ctx2 in
+    let eq_named_declaration d1 d2 =
+      match d1, d2 with
+      | LocalAssum (i1,t1), LocalAssum (i2,t2) ->
+         Names.Id.equal i1 i2 && eq_constr sigma1 sigma2 t1 t2
+      | LocalDef (i1,c1,t1), LocalDef (i2,c2,t2) ->
+         Names.Id.equal i1 i2 && eq_constr sigma1 sigma2 c1 c2
+         && eq_constr sigma1 sigma2 t1 t2
+      | _ ->
+         false
+    in List.equal eq_named_declaration c1 c2
+
+  let eq_evar_body sigma1 sigma2 b1 b2 =
+    let open Evd in
+    match b1, b2 with
+    | Evar_empty, Evar_empty -> true
+    | Evar_defined t1, Evar_defined t2 -> eq_constr sigma1 sigma2 t1 t2
+    | _ -> false
+
+  let eq_evar_info sigma1 sigma2 ei1 ei2 =
+    let open Evd in
+    eq_constr sigma1 sigma2 ei1.evar_concl ei2.evar_concl &&
+    eq_named_context_val sigma1 sigma2 (ei1.evar_hyps) (ei2.evar_hyps) &&
+    eq_evar_body sigma1 sigma2 ei1.evar_body ei2.evar_body
+
+  (** Equality function on goals *)
+  let goal_equal evars1 gl1 evars2 gl2 =
+    let evi1 = Evd.find evars1 gl1 in
+    let evi2 = Evd.find evars2 gl2 in
+    eq_evar_info evars1 evars2 evi1 evi2
+
+end
+
+let tclPROGRESS t =
+  let open Proof in
+  Pv.get >>= fun initial ->
+  t >>= fun res ->
+  Pv.get >>= fun final ->
+  (* [*_test] test absence of progress. [quick_test] is approximate
+     whereas [exhaustive_test] is complete. *)
+  let quick_test =
+    initial.solution == final.solution && initial.comb == final.comb
+  in
+  let exhaustive_test =
+    Util.List.for_all2eq begin fun i f ->
+      Progress.goal_equal initial.solution i final.solution f
+    end initial.comb final.comb
+  in
+  let test =
+    quick_test || exhaustive_test
+  in
+  if not test then
+    tclUNIT res
+  else
+    tclZERO (Errors.UserError ("Proofview.tclPROGRESS" , Pp.str"Failed to progress."))
+
+exception Timeout
+let _ = Errors.register_handler begin function
+  | Timeout -> Errors.errorlabstrm "Proofview.tclTIMEOUT" (Pp.str"Tactic timeout!")
+  | _ -> Pervasives.raise Errors.Unhandled
+end
+
+let tclTIMEOUT n t =
+  let open Proof in
+  (* spiwack: as one of the monad is a continuation passing monad, it
+     doesn't force the computation to be threaded inside the underlying
+     (IO) monad. Hence I force it myself by asking for the evaluation of
+     a dummy value first, lest [timeout] be called when everything has
+     already been computed. *)
+  let t = Proof.lift (Logic_monad.NonLogical.return ()) >> t in
+  Proof.get >>= fun initial ->
+  Proof.current >>= fun envvar ->
+  Proof.lift begin
+    Logic_monad.NonLogical.catch
+      begin
+        let open Logic_monad.NonLogical in
+        timeout n (Proof.repr (Proof.run t envvar initial)) >>= fun r ->
+        match r with
+        | Logic_monad.Nil e -> return (Util.Inr e)
+        | Logic_monad.Cons (r, _) -> return (Util.Inl r)
+      end
+      begin let open Logic_monad.NonLogical in function (e, info) ->
+        match e with
+        | Logic_monad.Timeout -> return (Util.Inr (Timeout, info))
+        | Logic_monad.TacticFailure e ->
+          return (Util.Inr (e, info))
+        | e -> Logic_monad.NonLogical.raise ~info e
+      end
+  end >>= function
+    | Util.Inl (res,s,m,i) ->
+        Proof.set s >>
+        Proof.put m >>
+        Proof.update (fun _ -> i) >>
+        return res
+    | Util.Inr (e, info) -> tclZERO ~info e
+
+let tclTIME s t =
+  let pr_time t1 t2 n msg =
+    let msg =
+      if n = 0 then
+        str msg
+      else
+        str (msg ^ " after ") ++ int n ++ str (String.plural n " backtracking")
+    in
+    msg_info(str "Tactic call" ++ pr_opt str s ++ str " ran for " ++
+             System.fmt_time_difference t1 t2 ++ str " " ++ surround msg) in
+  let rec aux n t =
+    let open Proof in
+    tclUNIT () >>= fun () ->
+    let tstart = System.get_time() in
+    Proof.split t >>= let open Logic_monad in function
+    | Nil (e, info) ->
+      begin
+        let tend = System.get_time() in
+        pr_time tstart tend n "failure";
+        tclZERO ~info e
+      end
+    | Cons (x,k) ->
+        let tend = System.get_time() in
+        pr_time tstart tend n "success";
+        tclOR (tclUNIT x) (fun e -> aux (n+1) (k e))
+  in aux 0 t
+
+
+
+(** {7 Unsafe primitives} *)
+
+module Unsafe = struct
+
+  let tclEVARS evd =
+    Pv.modify (fun ps -> { ps with solution = evd })
+
+  let tclNEWGOALS gls =
+    Pv.modify begin fun step ->
+      let gls = undefined step.solution gls in
+      { step with comb = step.comb @ gls }
+    end
+
+  let tclGETGOALS = Comb.get
+
+  let tclSETGOALS = Comb.set
+
+  let tclEVARSADVANCE evd =
+    Pv.modify (fun ps -> { ps with solution = evd; comb = undefined evd ps.comb })
+
+  let tclEVARUNIVCONTEXT ctx = 
+    Pv.modify (fun ps -> { ps with solution = Evd.set_universe_context ps.solution ctx })
+
+  let reset_future_goals p =
+    { p with solution = Evd.reset_future_goals p.solution }
+
+  let mark_as_goal evd content =
+    let info = Evd.find evd content in
+    let info =
+      { info with Evd.evar_source = match info.Evd.evar_source with
+      | _, (Evar_kinds.VarInstance _ | Evar_kinds.GoalEvar) as x -> x
+      | loc,_ -> loc,Evar_kinds.GoalEvar }
+    in
+    let info = match Evd.Store.get info.Evd.evar_extra typeclass_resolvable with
+    | None -> { info with Evd.evar_extra = Evd.Store.set info.Evd.evar_extra typeclass_resolvable () }
+    | Some () -> info
+    in
+    Evd.add evd content info
+
+  let advance = advance
+
+  let typeclass_resolvable = typeclass_resolvable
+
+end
+
+module UnsafeRepr = Proof.Unsafe
+
+let (>>=) = tclBIND
+let (<*>) = tclTHEN
+let (<+>) t1 t2 = tclOR t1 (fun _ -> t2)
+
+(** {6 Goal-dependent tactics} *)
+
+let goal_env evars gl =
+  let evi = Evd.find evars gl in
+  Evd.evar_filtered_env evi
+
+let goal_nf_evar sigma gl =
+  let evi = Evd.find sigma gl in
+  let evi = Evarutil.nf_evar_info sigma evi in
+  let sigma = Evd.add sigma gl evi in
+  (gl, sigma)
+
+let goal_extra evars gl =
+  let evi = Evd.find evars gl in
+  evi.Evd.evar_extra
+
+
+let catchable_exception = function
+  | Logic_monad.Exception _ -> false
+  | e -> Errors.noncritical e
+
+
+module Goal = struct
+
+  type ('a, 'r) t = {
+    env : Environ.env;
+    sigma : Evd.evar_map;
+    concl : Term.constr ;
+    self : Evar.t ; (* for compatibility with old-style definitions *)
+  }
+
+  type ('a, 'b) enter =
+    { enter : 'r. ('a, 'r) t -> 'b }
+
+  let assume (gl : ('a, 'r) t) = (gl :> ([ `NF ], 'r) t)
+
+  let env { env=env } = env
+  let sigma { sigma=sigma } = Sigma.Unsafe.of_evar_map sigma
+  let hyps { env=env } = Environ.named_context env
+  let concl { concl=concl } = concl
+  let extra { sigma=sigma; self=self } = goal_extra sigma self
+
+  let raw_concl { concl=concl } = concl
+
+
+  let gmake_with info env sigma goal = 
+    { env = Environ.reset_with_named_context (Evd.evar_filtered_hyps info) env ;
+      sigma = sigma ;
+      concl = Evd.evar_concl info ;
+      self = goal }
+
+  let nf_gmake env sigma goal =
+    let info = Evarutil.nf_evar_info sigma (Evd.find sigma goal) in
+    let sigma = Evd.add sigma goal info in
+    gmake_with info env sigma goal , sigma
+
+  let nf_enter f =
+    InfoL.tag (Info.Dispatch) begin
+    iter_goal begin fun goal ->
+      Env.get >>= fun env ->
+      tclEVARMAP >>= fun sigma ->
+      try
+        let (gl, sigma) = nf_gmake env sigma goal in
+        tclTHEN (Unsafe.tclEVARS sigma) (InfoL.tag (Info.DBranch) (f.enter gl))
+      with e when catchable_exception e ->
+        let (e, info) = Errors.push e in
+        tclZERO ~info e
+    end
+    end
+
+  let normalize { self } =
+    Env.get >>= fun env ->
+    tclEVARMAP >>= fun sigma ->
+    let (gl,sigma) = nf_gmake env sigma self in
+    tclTHEN (Unsafe.tclEVARS sigma) (tclUNIT gl)
+
+  let gmake env sigma goal =
+    let info = Evd.find sigma goal in
+    gmake_with info env sigma goal
+
+  let enter f =
+    let f gl = InfoL.tag (Info.DBranch) (f.enter gl) in
+    InfoL.tag (Info.Dispatch) begin
+    iter_goal begin fun goal ->
+      Env.get >>= fun env ->
+      tclEVARMAP >>= fun sigma ->
+      try f (gmake env sigma goal)
+      with e when catchable_exception e ->
+        let (e, info) = Errors.push e in
+        tclZERO ~info e
+    end
+    end
+
+  type ('a, 'b) s_enter =
+    { s_enter : 'r. ('a, 'r) t -> ('b, 'r) Sigma.sigma }
+
+  let s_enter f =
+    InfoL.tag (Info.Dispatch) begin
+    iter_goal begin fun goal ->
+      Env.get >>= fun env ->
+      tclEVARMAP >>= fun sigma ->
+      try
+        let gl = gmake env sigma goal in
+        let Sigma (tac, sigma, _) = f.s_enter gl in
+        let sigma = Sigma.to_evar_map sigma in
+        tclTHEN (Unsafe.tclEVARS sigma) (InfoL.tag (Info.DBranch) tac)
+      with e when catchable_exception e ->
+        let (e, info) = Errors.push e in
+        tclZERO ~info e
+    end
+    end
+
+  let nf_s_enter f =
+    InfoL.tag (Info.Dispatch) begin
+    iter_goal begin fun goal ->
+      Env.get >>= fun env ->
+      tclEVARMAP >>= fun sigma ->
+      try
+        let (gl, sigma) = nf_gmake env sigma goal in
+        let Sigma (tac, sigma, _) = f.s_enter gl in
+        let sigma = Sigma.to_evar_map sigma in
+        tclTHEN (Unsafe.tclEVARS sigma) (InfoL.tag (Info.DBranch) tac)
+      with e when catchable_exception e ->
+        let (e, info) = Errors.push e in
+        tclZERO ~info e
+    end
+    end
+
+  let goals =
+    Pv.get >>= fun step ->
+    let sigma = step.solution in
+    let map goal =
+      match advance sigma goal with
+      | None -> None (** ppedrot: Is this check really necessary? *)
+      | Some goal ->
+        let gl =
+          Env.get >>= fun env ->
+          tclEVARMAP >>= fun sigma ->
+          tclUNIT (gmake env sigma goal)
+        in
+        Some gl
+    in
+    tclUNIT (CList.map_filter map step.comb)
+
+  (* compatibility *)
+  let goal { self=self } = self
+
+  let lift (gl : ('a, 'r) t) _ = (gl :> ('a, 's) t)
+
+end
+
+
+
+(** {6 Trace} *)
+
+module Trace = struct
+
+  let record_info_trace = InfoL.record_trace
+
+  let log m = InfoL.leaf (Info.Msg m)
+  let name_tactic m t = InfoL.tag (Info.Tactic m) t
+
+  let pr_info ?(lvl=0) info =
+    assert (lvl >= 0);
+    Info.(print (collapse lvl info))
+
+end
+
+
+
+(** {6 Non-logical state} *)
+
+module NonLogical = Logic_monad.NonLogical
+
+let tclLIFT = Proof.lift
+
+let tclCHECKINTERRUPT =
+   tclLIFT (NonLogical.make Control.check_for_interrupt)
+
+
+
+
+
+(*** Compatibility layer with <= 8.2 tactics ***)
+module V82 = struct
+  type tac = Evar.t Evd.sigma -> Evar.t list Evd.sigma
+
+  let tactic tac =
+    (* spiwack: we ignore the dependencies between goals here,
+       expectingly preserving the semantics of <= 8.2 tactics *)
+    (* spiwack: convenience notations, waiting for ocaml 3.12 *)
+    let open Proof in
+    Pv.get >>= fun ps ->
+    try
+      let tac gl evd = 
+        let glsigma  =
+          tac { Evd.it = gl ; sigma = evd; }  in
+        let sigma = glsigma.Evd.sigma in
+        let g = glsigma.Evd.it in
+        ( g, sigma )
+      in
+        (* Old style tactics expect the goals normalized with respect to evars. *)
+      let (initgoals,initevd) =
+        Evd.Monad.List.map (fun g s -> goal_nf_evar s g) ps.comb ps.solution
+      in
+      let (goalss,evd) = Evd.Monad.List.map tac initgoals initevd in
+      let sgs = CList.flatten goalss in
+      let sgs = undefined evd sgs in
+      InfoL.leaf (Info.Tactic (fun () -> Pp.str"<unknown>")) >>
+      Pv.set { ps with solution = evd; comb = sgs; }
+    with e when catchable_exception e ->
+      let (e, info) = Errors.push e in
+      tclZERO ~info e
+
+
+  (* normalises the evars in the goals, and stores the result in
+     solution. *)
+  let nf_evar_goals =
+    Pv.modify begin fun ps ->
+    let map g s = goal_nf_evar s g in
+    let (goals,evd) = Evd.Monad.List.map map ps.comb ps.solution in
+    { ps with solution = evd; comb = goals; }
+    end
+      
+  let has_unresolved_evar pv =
+    Evd.has_undefined pv.solution
+
+  (* Main function in the implementation of Grab Existential Variables.*)
+  let grab pv =
+    let undef = Evd.undefined_map pv.solution in
+    let goals = CList.rev_map fst (Evar.Map.bindings undef) in
+    { pv with comb = goals }
+      
+    
+
+  (* Returns the open goals of the proofview together with the evar_map to 
+     interpret them. *)
+  let goals { comb = comb ; solution = solution; } =
+   { Evd.it = comb ; sigma = solution }
+
+  let top_goals initial { solution=solution; } =
+    let goals = CList.map (fun (t,_) -> fst (Term.destEvar t)) initial in
+    { Evd.it = goals ; sigma=solution; }
+
+  let top_evars initial =
+    let evars_of_initial (c,_) =
+      Evar.Set.elements (Evd.evars_of_term c)
+    in
+    CList.flatten (CList.map evars_of_initial initial)
+
+  let of_tactic t gls =
+    try
+      let init = { shelf = []; solution = gls.Evd.sigma ; comb = [gls.Evd.it] } in
+      let (_,final,_,_) = apply (goal_env gls.Evd.sigma gls.Evd.it) t init in
+      { Evd.sigma = final.solution ; it = final.comb }
+    with Logic_monad.TacticFailure e as src ->
+      let (_, info) = Errors.push src in
+      iraise (e, info)
+
+  let put_status = Status.put
+
+  let catchable_exception = catchable_exception
+
+  let wrap_exceptions f =
+    try f ()
+    with e when catchable_exception e ->
+      let (e, info) = Errors.push e in tclZERO ~info e
+
+end
+
+(** {7 Notations} *)
+
+module Notations = struct
+  let (>>=) = tclBIND
+  let (<*>) = tclTHEN
+  let (<+>) t1 t2 = tclOR t1 (fun _ -> t2)
+  type ('a, 'b) enter = ('a, 'b) Goal.enter =
+    { enter : 'r. ('a, 'r) Goal.t -> 'b }
+  type ('a, 'b) s_enter = ('a, 'b) Goal.s_enter =
+    { s_enter : 'r. ('a, 'r) Goal.t -> ('b, 'r) Sigma.sigma }
+end
diff --git a/engine/proofview.mli b/engine/proofview.mli
new file mode 100644
index 000000000..7996b7969
--- /dev/null
+++ b/engine/proofview.mli
@@ -0,0 +1,589 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(** This files defines the basic mechanism of proofs: the [proofview]
+    type is the state which tactics manipulate (a global state for
+    existential variables, together with the list of goals), and the type
+    ['a tactic] is the (abstract) type of tactics modifying the proof
+    state and returning a value of type ['a]. *)
+
+open Util
+open Term
+
+(** Main state of tactics *)
+type proofview
+
+(** Returns a stylised view of a proofview for use by, for instance,
+    ide-s. *)
+(* spiwack: the type of [proofview] will change as we push more
+   refined functions to ide-s. This would be better than spawning a
+   new nearly identical function everytime. Hence the generic name. *)
+(* In this version: returns the list of focused goals together with
+   the [evar_map] context. *)
+val proofview : proofview -> Goal.goal list * Evd.evar_map
+
+
+(** {6 Starting and querying a proof view} *)
+
+(** Abstract representation of the initial goals of a proof. *)
+type entry
+
+(** Optimize memory consumption *)
+val compact : entry -> proofview -> entry * proofview
+
+(** Initialises a proofview, the main argument is a list of
+    environments (including a [named_context] which are used as
+    hypotheses) pair with conclusion types, creating accordingly many
+    initial goals. Because a proof does not necessarily starts in an
+    empty [evar_map] (indeed a proof can be triggered by an incomplete
+    pretyping), [init] takes an additional argument to represent the
+    initial [evar_map]. *)
+val init : Evd.evar_map -> (Environ.env * Term.types) list -> entry * proofview
+
+(** A [telescope] is a list of environment and conclusion like in
+    {!init}, except that each element may depend on the previous
+    goals. The telescope passes the goals in the form of a
+    [Term.constr] which represents the goal as an [evar]. The
+    [evar_map] is threaded in state passing style. *)
+type telescope =
+  | TNil of Evd.evar_map
+  | TCons of Environ.env * Evd.evar_map * Term.types * (Evd.evar_map -> Term.constr -> telescope)
+
+(** Like {!init}, but goals are allowed to be dependent on one
+    another. Dependencies between goals is represented with the type
+    [telescope] instead of [list]. Note that the first [evar_map] of
+    the telescope plays the role of the [evar_map] argument in
+    [init]. *)
+val dependent_init  : telescope -> entry * proofview
+
+(** [finished pv] is [true] if and only if [pv] is complete. That is,
+    if it has an empty list of focused goals. There could still be
+    unsolved subgoaled, but they would then be out of focus. *)
+val finished : proofview -> bool
+
+(** Returns the current [evar] state. *)
+val return : proofview -> Evd.evar_map
+
+val partial_proof : entry -> proofview -> constr list
+val initial_goals : entry -> (constr * types) list
+
+
+
+(** {6 Focusing commands} *)
+
+(** A [focus_context] represents the part of the proof view which has
+    been removed by a focusing action, it can be used to unfocus later
+    on. *)
+type focus_context
+
+(** Returns a stylised view of a focus_context for use by, for
+    instance, ide-s. *)
+(* spiwack: the type of [focus_context] will change as we push more
+   refined functions to ide-s. This would be better than spawning a
+   new nearly identical function everytime. Hence the generic name. *)
+(* In this version: the goals in the context, as a "zipper" (the first
+   list is in reversed order). *)
+val focus_context : focus_context -> Goal.goal list * Goal.goal list
+
+(** [focus i j] focuses a proofview on the goals from index [i] to
+    index [j] (inclusive, goals are indexed from [1]). I.e. goals
+    number [i] to [j] become the only focused goals of the returned
+    proofview.  It returns the focused proofview, and a context for
+    the focus stack. *)
+val focus : int -> int -> proofview -> proofview * focus_context
+
+(** Unfocuses a proofview with respect to a context. *)
+val unfocus : focus_context -> proofview -> proofview
+
+
+(** {6 The tactic monad} *)
+
+(** - Tactics are objects which apply a transformation to all the
+    subgoals of the current view at the same time. By opposition to
+    the old vision of applying it to a single goal. It allows tactics
+    such as [shelve_unifiable], tactics to reorder the focused goals,
+    or global automation tactic for dependent subgoals (instantiating
+    an evar has influences on the other goals of the proof in
+    progress, not being able to take that into account causes the
+    current eauto tactic to fail on some instances where it could
+    succeed).  Another benefit is that it is possible to write tactics
+    that can be executed even if there are no focused goals.
+    - Tactics form a monad ['a tactic], in a sense a tactic can be
+    seen as a function (without argument) which returns a value of
+    type 'a and modifies the environment (in our case: the view).
+    Tactics of course have arguments, but these are given at the
+    meta-level as OCaml functions.  Most tactics in the sense we are
+    used to return [()], that is no really interesting values. But
+    some might pass information around.  The tactics seen in Coq's
+    Ltac are (for now at least) only [unit tactic], the return values
+    are kept for the OCaml toolkit.  The operation or the monad are
+    [Proofview.tclUNIT] (which is the "return" of the tactic monad)
+    [Proofview.tclBIND] (which is the "bind") and [Proofview.tclTHEN]
+    (which is a specialized bind on unit-returning tactics).
+    - Tactics have support for full-backtracking. Tactics can be seen
+    having multiple success: if after returning the first success a
+    failure is encountered, the tactic can backtrack and use a second
+    success if available. The state is backtracked to its previous
+    value, except the non-logical state defined in the {!NonLogical}
+    module below.
+*)
+
+
+(** The abstract type of tactics *)
+type +'a tactic 
+
+(** Applies a tactic to the current proofview. Returns a tuple
+    [a,pv,(b,sh,gu)] where [a] is the return value of the tactic, [pv]
+    is the updated proofview, [b] a boolean which is [true] if the
+    tactic has not done any action considered unsafe (such as
+    admitting a lemma), [sh] is the list of goals which have been
+    shelved by the tactic, and [gu] the list of goals on which the
+    tactic has given up. In case of multiple success the first one is
+    selected. If there is no success, fails with
+    {!Logic_monad.TacticFailure}*)
+val apply : Environ.env -> 'a tactic -> proofview -> 'a
+                                                   * proofview
+                                                   * (bool*Goal.goal list*Goal.goal list)
+                                                   * Proofview_monad.Info.tree
+
+(** {7 Monadic primitives} *)
+
+(** Unit of the tactic monad. *)
+val tclUNIT : 'a -> 'a tactic
+ 
+(** Bind operation of the tactic monad. *)
+val tclBIND : 'a tactic -> ('a -> 'b tactic) -> 'b tactic
+
+(** Interprets the ";" (semicolon) of Ltac. As a monadic operation,
+    it's a specialized "bind". *)
+val tclTHEN : unit tactic -> 'a tactic -> 'a tactic
+
+(** [tclIGNORE t] has the same operational content as [t], but drops
+    the returned value. *)
+val tclIGNORE : 'a tactic -> unit tactic
+
+(** Generic monadic combinators for tactics. *)
+module Monad : Monad.S with type +'a t = 'a tactic
+
+(** {7 Failure and backtracking} *)
+
+(** [tclZERO e] fails with exception [e]. It has no success. *)
+val tclZERO : ?info:Exninfo.info -> exn -> 'a tactic
+
+(** [tclOR t1 t2] behaves like [t1] as long as [t1] succeeds. Whenever
+    the successes of [t1] have been depleted and it failed with [e],
+    then it behaves as [t2 e]. In other words, [tclOR] inserts a
+    backtracking point. *)
+val tclOR : 'a tactic -> (iexn -> 'a tactic) -> 'a tactic
+
+(** [tclORELSE t1 t2] is equal to [t1] if [t1] has at least one
+    success or [t2 e] if [t1] fails with [e]. It is analogous to
+    [try/with] handler of exception in that it is not a backtracking
+    point. *)
+val tclORELSE : 'a tactic -> (iexn -> 'a tactic) -> 'a tactic
+
+(** [tclIFCATCH a s f] is a generalisation of {!tclORELSE}: if [a]
+    succeeds at least once then it behaves as [tclBIND a s] otherwise,
+    if [a] fails with [e], then it behaves as [f e]. *)
+val tclIFCATCH : 'a tactic -> ('a -> 'b tactic) -> (iexn -> 'b tactic) -> 'b tactic
+
+(** [tclONCE t] behave like [t] except it has at most one success:
+    [tclONCE t] stops after the first success of [t]. If [t] fails
+    with [e], [tclONCE t] also fails with [e]. *)
+val tclONCE : 'a tactic -> 'a tactic
+
+(** [tclEXACTLY_ONCE e t] succeeds as [t] if [t] has exactly one
+    success. Otherwise it fails. The tactic [t] is run until its first
+    success, then a failure with exception [e] is simulated. It [t]
+    yields another success, then [tclEXACTLY_ONCE e t] fails with
+    [MoreThanOneSuccess] (it is a user error). Otherwise,
+    [tclEXACTLY_ONCE e t] succeeds with the first success of
+    [t]. Notice that the choice of [e] is relevant, as the presence of
+    further successes may depend on [e] (see {!tclOR}). *)
+exception MoreThanOneSuccess
+val tclEXACTLY_ONCE : exn -> 'a tactic -> 'a tactic
+
+(** [tclCASE t] splits [t] into its first success and a
+    continuation. It is the most general primitive to control
+    backtracking. *)
+type 'a case =
+  | Fail of iexn
+  | Next of 'a * (iexn -> 'a tactic)
+val tclCASE : 'a tactic -> 'a case tactic
+
+(** [tclBREAK p t] is a generalization of [tclONCE t]. Instead of
+    stopping after the first success, it succeeds like [t] until a
+    failure with an exception [e] such that [p e = Some e'] is raised. At
+    which point it drops the remaining successes, failing with [e'].
+    [tclONCE t] is equivalent to [tclBREAK (fun e -> Some e) t]. *)
+val tclBREAK : (iexn -> iexn option) -> 'a tactic -> 'a tactic
+
+
+(** {7 Focusing tactics} *)
+
+(** [tclFOCUS i j t] applies [t] after focusing on the goals number
+    [i] to [j] (see {!focus}). The rest of the goals is restored after
+    the tactic action. If the specified range doesn't correspond to
+    existing goals, fails with [NoSuchGoals] (a user error). this
+    exception is caught at toplevel with a default message + a hook
+    message that can be customized by [set_nosuchgoals_hook] below.
+    This hook is used to add a suggestion about bullets when
+    applicable. *)
+exception NoSuchGoals of int
+val set_nosuchgoals_hook: (int -> Pp.std_ppcmds) -> unit
+
+val tclFOCUS : int -> int -> 'a tactic -> 'a tactic
+
+(** [tclFOCUSID x t] applies [t] on a (single) focused goal like
+    {!tclFOCUS}. The goal is found by its name rather than its
+    number.*)
+val tclFOCUSID : Names.Id.t -> 'a tactic -> 'a tactic
+
+(** [tclTRYFOCUS i j t] behaves like {!tclFOCUS}, except that if the
+    specified range doesn't correspond to existing goals, behaves like
+    [tclUNIT ()] instead of failing. *)
+val tclTRYFOCUS : int -> int -> unit tactic -> unit tactic
+
+
+(** {7 Dispatching on goals} *)
+
+(** Dispatch tacticals are used to apply a different tactic to each
+    goal under focus. They come in two flavours: [tclDISPATCH] takes a
+    list of [unit tactic]-s and build a [unit tactic]. [tclDISPATCHL]
+    takes a list of ['a tactic] and returns an ['a list tactic].
+
+    They both work by applying each of the tactic in a focus
+    restricted to the corresponding goal (starting with the first
+    goal). In the case of [tclDISPATCHL], the tactic returns a list of
+    the same size as the argument list (of tactics), each element
+    being the result of the tactic executed in the corresponding goal.
+
+    When the length of the tactic list is not the number of goal,
+    raises [SizeMismatch (g,t)] where [g] is the number of available
+    goals, and [t] the number of tactics passed. *)
+exception SizeMismatch of int*int
+val tclDISPATCH : unit tactic list -> unit tactic
+val tclDISPATCHL : 'a tactic list -> 'a list tactic
+
+(** [tclEXTEND b r e] is a variant of {!tclDISPATCH}, where the [r]
+    tactic is "repeated" enough time such that every goal has a tactic
+    assigned to it ([b] is the list of tactics applied to the first
+    goals, [e] to the last goals, and [r] is applied to every goal in
+    between). *)
+val tclEXTEND : unit tactic list -> unit tactic -> unit tactic list -> unit tactic
+
+(** [tclINDEPENDENT tac] runs [tac] on each goal successively, from
+    the first one to the last one. Backtracking in one goal is
+    independent of backtracking in another. It is equivalent to
+    [tclEXTEND [] tac []]. *)
+val tclINDEPENDENT : unit tactic -> unit tactic
+
+
+(** {7 Goal manipulation} *)
+
+(** Shelves all the goals under focus. The goals are placed on the
+    shelf for later use (or being solved by side-effects). *)
+val shelve : unit tactic
+
+(** Shelves the unifiable goals under focus, i.e. the goals which
+    appear in other goals under focus (the unfocused goals are not
+    considered). *)
+val shelve_unifiable : unit tactic
+
+(** [guard_no_unifiable] returns the list of unifiable goals if some
+    goals are unifiable (see {!shelve_unifiable}) in the current focus. *)
+val guard_no_unifiable : Names.Name.t list option tactic
+
+(** [unshelve l p] adds all the goals in [l] at the end of the focused
+    goals of p *)
+val unshelve : Goal.goal list -> proofview -> proofview
+
+(** [with_shelf tac] executes [tac] and returns its result together with the set
+    of goals shelved by [tac]. The current shelf is unchanged. *)
+val with_shelf : 'a tactic -> (Goal.goal list * 'a) tactic
+
+(** If [n] is positive, [cycle n] puts the [n] first goal last. If [n]
+    is negative, then it puts the [n] last goals first.*)
+val cycle : int -> unit tactic
+
+(** [swap i j] swaps the position of goals number [i] and [j]
+    (negative numbers can be used to address goals from the end. Goals
+    are indexed from [1]. For simplicity index [0] corresponds to goal
+    [1] as well, rather than raising an error. *)
+val swap : int -> int -> unit tactic
+
+(** [revgoals] reverses the list of focused goals. *)
+val revgoals : unit tactic
+
+(** [numgoals] returns the number of goals under focus. *)
+val numgoals : int tactic
+
+
+(** {7 Access primitives} *)
+
+(** [tclEVARMAP] doesn't affect the proof, it returns the current
+    [evar_map]. *)
+val tclEVARMAP : Evd.evar_map tactic
+
+(** [tclENV] doesn't affect the proof, it returns the current
+    environment. It is not the environment of a particular goal,
+    rather the "global" environment of the proof. The goal-wise
+    environment is obtained via {!Proofview.Goal.env}. *)
+val tclENV : Environ.env tactic
+
+
+(** {7 Put-like primitives} *)
+
+(** [tclEFFECTS eff] add the effects [eff] to the current state. *)
+val tclEFFECTS : Safe_typing.private_constants -> unit tactic
+
+(** [mark_as_unsafe] declares the current tactic is unsafe. *)
+val mark_as_unsafe : unit tactic
+
+(** Gives up on the goal under focus. Reports an unsafe status. Proofs
+    with given up goals cannot be closed. *)
+val give_up : unit tactic
+
+
+(** {7 Control primitives} *)
+
+(** [tclPROGRESS t] checks the state of the proof after [t]. It it is
+    identical to the state before, then [tclePROGRESS t] fails, otherwise
+    it succeeds like [t]. *)
+val tclPROGRESS : 'a tactic -> 'a tactic
+
+(** Checks for interrupts *)
+val tclCHECKINTERRUPT : unit tactic
+
+exception Timeout
+(** [tclTIMEOUT n t] can have only one success.
+    In case of timeout if fails with [tclZERO Timeout]. *)
+val tclTIMEOUT : int -> 'a tactic -> 'a tactic
+
+(** [tclTIME s t] displays time for each atomic call to t, using s as an
+    identifying annotation if present *)
+val tclTIME : string option -> 'a tactic -> 'a tactic
+
+(** {7 Unsafe primitives} *)
+
+(** The primitives in the [Unsafe] module should be avoided as much as
+    possible, since they can make the proof state inconsistent. They are
+    nevertheless helpful, in particular when interfacing the pretyping and
+    the proof engine. *)
+module Unsafe : sig
+
+  (** [tclEVARS sigma] replaces the current [evar_map] by [sigma]. If
+      [sigma] has new unresolved [evar]-s they will not appear as
+      goal. If goals have been solved in [sigma] they will still
+      appear as unsolved goals. *)
+  val tclEVARS : Evd.evar_map -> unit tactic
+    
+  (** Like {!tclEVARS} but also checks whether goals have been solved. *)
+  val tclEVARSADVANCE : Evd.evar_map -> unit tactic
+
+  (** [tclNEWGOALS gls] adds the goals [gls] to the ones currently
+      being proved, appending them to the list of focused goals. If a
+      goal is already solved, it is not added. *)
+  val tclNEWGOALS : Goal.goal list -> unit tactic
+
+  (** [tclSETGOALS gls] sets goals [gls] as the goals being under focus. If a
+      goal is already solved, it is not set. *)
+  val tclSETGOALS : Goal.goal list -> unit tactic
+
+  (** [tclGETGOALS] returns the list of goals under focus. *)
+  val tclGETGOALS : Goal.goal list tactic
+
+  (** Sets the evar universe context. *)
+  val tclEVARUNIVCONTEXT : Evd.evar_universe_context -> unit tactic
+
+  (** Clears the future goals store in the proof view. *)
+  val reset_future_goals : proofview -> proofview
+
+  (** Give an evar the status of a goal (changes its source location
+      and makes it unresolvable for type classes. *)
+  val mark_as_goal : Evd.evar_map -> Evar.t -> Evd.evar_map
+
+  (** [advance sigma g] returns [Some g'] if [g'] is undefined and is
+      the current avatar of [g] (for instance [g] was changed by [clear]
+      into [g']). It returns [None] if [g] has been (partially)
+      solved. *)
+  val advance : Evd.evar_map -> Evar.t -> Evar.t option
+
+  val typeclass_resolvable : unit Evd.Store.field
+
+end
+
+(** This module gives access to the innards of the monad. Its use is
+    restricted to very specific cases. *)
+module UnsafeRepr :
+sig
+  type state = Proofview_monad.Logical.Unsafe.state
+  val repr : 'a tactic -> ('a, state, state, iexn) Logic_monad.BackState.t
+  val make : ('a, state, state, iexn) Logic_monad.BackState.t -> 'a tactic
+end
+
+(** {6 Goal-dependent tactics} *)
+
+module Goal : sig
+
+  (** Type of goals.
+
+      The first parameter type is a phantom argument indicating whether the data
+      contained in the goal has been normalized w.r.t. the current sigma. If it
+      is the case, it is flagged [ `NF ]. You may still access the un-normalized
+      data using {!assume} if you known you do not rely on the assumption of
+      being normalized, at your own risk.
+
+      The second parameter is a stage indicating where the goal belongs. See
+      module {!Sigma}.
+  *)
+  type ('a, 'r) t
+
+  (** Assume that you do not need the goal to be normalized. *)
+  val assume : ('a, 'r) t -> ([ `NF ], 'r) t
+
+  (** Normalises the argument goal. *)
+  val normalize : ('a, 'r) t -> ([ `NF ], 'r) t tactic
+
+  (** [concl], [hyps], [env] and [sigma] given a goal [gl] return
+      respectively the conclusion of [gl], the hypotheses of [gl], the
+      environment of [gl] (i.e. the global environment and the
+      hypotheses) and the current evar map. *)
+  val concl : ([ `NF ], 'r) t -> Term.constr
+  val hyps : ([ `NF ], 'r) t -> Context.Named.t
+  val env : ('a, 'r) t -> Environ.env
+  val sigma : ('a, 'r) t -> 'r Sigma.t
+  val extra : ('a, 'r) t -> Evd.Store.t
+
+  (** Returns the goal's conclusion even if the goal is not
+      normalised. *)
+  val raw_concl : ('a, 'r) t -> Term.constr
+
+  type ('a, 'b) enter =
+    { enter : 'r. ('a, 'r) t -> 'b }
+
+  (** [nf_enter t] applies the goal-dependent tactic [t] in each goal
+      independently, in the manner of {!tclINDEPENDENT} except that
+      the current goal is also given as an argument to [t]. The goal
+      is normalised with respect to evars. *)
+  val nf_enter : ([ `NF ], unit tactic) enter -> unit tactic
+
+  (** Like {!nf_enter}, but does not normalize the goal beforehand. *)
+  val enter : ([ `LZ ], unit tactic) enter -> unit tactic
+
+  type ('a, 'b) s_enter =
+    { s_enter : 'r. ('a, 'r) t -> ('b, 'r) Sigma.sigma }
+
+  (** A variant of {!enter} allows to work with a monotonic state. The evarmap
+      returned by the argument is put back into the current state before firing
+      the returned tactic. *)
+  val s_enter : ([ `LZ ], unit tactic) s_enter -> unit tactic
+
+  (** Like {!s_enter}, but normalizes the goal beforehand. *)
+  val nf_s_enter : ([ `NF ], unit tactic) s_enter -> unit tactic
+
+  (** Recover the list of current goals under focus, without evar-normalization.
+      FIXME: encapsulate the level in an existential type. *)
+  val goals : ([ `LZ ], 'r) t tactic list tactic
+
+  (** Compatibility: avoid if possible *)
+  val goal : ([ `NF ], 'r) t -> Evar.t
+
+  (** Every goal is valid at a later stage. FIXME: take a later evarmap *)
+  val lift : ('a, 'r) t -> ('r, 's) Sigma.le -> ('a, 's) t
+
+end
+
+
+(** {6 Trace} *)
+
+module Trace : sig
+
+  (** [record_info_trace t] behaves like [t] except the [info] trace
+      is stored. *)
+  val record_info_trace : 'a tactic -> 'a tactic
+
+  val log : Proofview_monad.lazy_msg -> unit tactic
+  val name_tactic : Proofview_monad.lazy_msg -> 'a tactic -> 'a tactic
+
+  val pr_info : ?lvl:int -> Proofview_monad.Info.tree -> Pp.std_ppcmds
+
+end
+
+
+(** {6 Non-logical state} *)
+
+(** The [NonLogical] module allows the execution of effects (including
+    I/O) in tactics (non-logical side-effects are not discarded at
+    failures). *)
+module NonLogical : module type of Logic_monad.NonLogical
+
+(** [tclLIFT c] is a tactic which behaves exactly as [c]. *)
+val tclLIFT : 'a NonLogical.t -> 'a tactic
+
+
+(**/**)
+
+(*** Compatibility layer with <= 8.2 tactics ***)
+module V82 : sig
+  type tac = Evar.t Evd.sigma -> Evar.t list Evd.sigma
+  val tactic : tac -> unit tactic
+
+  (* normalises the evars in the goals, and stores the result in
+     solution. *)
+  val nf_evar_goals : unit tactic
+
+  val has_unresolved_evar : proofview -> bool
+
+  (* Main function in the implementation of Grab Existential Variables.
+     Resets the proofview's goals so that it contains all unresolved evars
+     (in chronological order of insertion). *)
+  val grab : proofview -> proofview
+
+  (* Returns the open goals of the proofview together with the evar_map to 
+     interpret them. *)
+  val goals : proofview -> Evar.t list Evd.sigma
+
+  val top_goals : entry -> proofview -> Evar.t list Evd.sigma
+  
+  (* returns the existential variable used to start the proof *)
+  val top_evars : entry -> Evd.evar list
+
+  (* Caution: this function loses quite a bit of information. It
+     should be avoided as much as possible.  It should work as
+     expected for a tactic obtained from {!V82.tactic} though. *)
+  val of_tactic : 'a tactic -> tac
+
+  (* marks as unsafe if the argument is [false] *)
+  val put_status : bool -> unit tactic
+
+  (* exception for which it is deemed to be safe to transmute into
+     tactic failure. *)
+  val catchable_exception : exn -> bool
+
+  (* transforms every Ocaml (catchable) exception into a failure in
+     the monad. *)
+  val wrap_exceptions : (unit -> 'a tactic) -> 'a tactic
+end
+
+(** {7 Notations} *)
+
+module Notations : sig
+
+  (** {!tclBIND} *)
+  val (>>=) : 'a tactic -> ('a -> 'b tactic) -> 'b tactic
+  (** {!tclTHEN} *)
+  val (<*>) : unit tactic -> 'a tactic -> 'a tactic
+  (** {!tclOR}: [t1+t2] = [tclOR t1 (fun _ -> t2)]. *)
+  val (<+>) : 'a tactic -> 'a tactic -> 'a tactic
+
+  type ('a, 'b) enter = ('a, 'b) Goal.enter =
+    { enter : 'r. ('a, 'r) Goal.t -> 'b }
+  type ('a, 'b) s_enter = ('a, 'b) Goal.s_enter =
+    { s_enter : 'r. ('a, 'r) Goal.t -> ('b, 'r) Sigma.sigma }
+end