Extension of the recursive notations mechanism

- Added support for recursive notations with binders
- Added support for arbitrary large iterators in recursive notations
- More checks on the use of variables and improved error messages
- Do side-effects in metasyntax only when sure that everything is ok
- Documentation

Note: it seems there were a small bug in match_alist (instances obtained
from matching the first copy of iterator were not propagated).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13316 85f007b7-540e-0410-9357-904b9bb8a0f7

10 files changed, 633 insertions, 326 deletions

diff --git a/interp/constrextern.ml b/interp/constrextern.ml
index 95a669f75..1c76aabbc 100644
--- a/interp/constrextern.ml
+++ b/interp/constrextern.ml
@@ -176,9 +176,10 @@ let rec check_same_type ty1 ty2 =
       check_same_type b1 b2
   | CCast(_,a1,CastCoerce), CCast(_,a2, CastCoerce) ->
       check_same_type a1 a2
-  | CNotation(_,n1,(e1,el1)), CNotation(_,n2,(e2,el2)) when n1=n2 ->
+  | CNotation(_,n1,(e1,el1,bl1)), CNotation(_,n2,(e2,el2,bl2)) when n1=n2 ->
       List.iter2 check_same_type e1 e2;
-      List.iter2 (List.iter2 check_same_type) el1 el2
+      List.iter2 (List.iter2 check_same_type) el1 el2;
+      List.iter2 check_same_fix_binder bl1 bl2
   | CPrim(_,i1), CPrim(_,i2) when i1=i2 -> ()
   | CDelimiters(_,s1,e1), CDelimiters(_,s2,e2) when s1=s2 ->
       check_same_type e1 e2
@@ -285,7 +286,7 @@ and spaces ntn n =
   if n = String.length ntn then []
   else if ntn.[n] = ' ' then wildcards ntn (n+1) else spaces ntn (n+1)
 
-let expand_curly_brackets loc mknot ntn (l,ll) =
+let expand_curly_brackets loc mknot ntn l =
   let ntn' = ref ntn in
   let rec expand_ntn i =
     function
@@ -298,12 +299,12 @@ let expand_curly_brackets loc mknot ntn (l,ll) =
             ntn' :=
               String.sub !ntn' 0 p ^ "_" ^
               String.sub !ntn' (p+5) (String.length !ntn' -p-5);
-            mknot (loc,"{ _ }",([a],[])) end
+            mknot (loc,"{ _ }",[a]) end
           else a in
         a' :: expand_ntn (i+1) l in
   let l = expand_ntn 0 l in
   (* side effect *)
-  mknot (loc,!ntn',(l,ll))
+  mknot (loc,!ntn',l)
 
 let destPrim = function CPrim(_,t) -> Some t | _ -> None
 let destPatPrim = function CPatPrim(_,t) -> Some t | _ -> None
@@ -311,32 +312,34 @@ let destPatPrim = function CPatPrim(_,t) -> Some t | _ -> None
 let make_notation_gen loc ntn mknot mkprim destprim l =
   if has_curly_brackets ntn
   then expand_curly_brackets loc mknot ntn l
-  else match ntn,List.map destprim (fst l),(snd l) with
+  else match ntn,List.map destprim l with
     (* Special case to avoid writing "- 3" for e.g. (Zopp 3) *)
-    | "- _", [Some (Numeral p)],[] when Bigint.is_strictly_pos p ->
-        mknot (loc,ntn,([mknot (loc,"( _ )",l)],[]))
+    | "- _", [Some (Numeral p)] when Bigint.is_strictly_pos p ->
+        mknot (loc,ntn,([mknot (loc,"( _ )",l)]))
     | _ ->
 	match decompose_notation_key ntn, l with
-	| [Terminal "-"; Terminal x], ([],[]) ->
+	| [Terminal "-"; Terminal x], [] ->
 	    (try mkprim (loc, Numeral (Bigint.neg (Bigint.of_string x)))
- 	     with _ -> mknot (loc,ntn,([],[])))
-	| [Terminal x], ([],[]) ->
+	     with _ -> mknot (loc,ntn,[]))
+	| [Terminal x], [] ->
 	    (try mkprim (loc, Numeral (Bigint.of_string x))
- 	     with _ -> mknot (loc,ntn,([],[])))
+	     with _ -> mknot (loc,ntn,[]))
 	| _ ->
 	    mknot (loc,ntn,l)
 
-let make_notation loc ntn l =
+let make_notation loc ntn (terms,termlists,binders as subst) =
+  if termlists <> [] or binders <> [] then CNotation (loc,ntn,subst) else
   make_notation_gen loc ntn
-    (fun (loc,ntn,l) -> CNotation (loc,ntn,l))
+    (fun (loc,ntn,l) -> CNotation (loc,ntn,(l,[],[])))
     (fun (loc,p) -> CPrim (loc,p))
-    destPrim l
+    destPrim terms
 
-let make_pat_notation loc ntn l =
+let make_pat_notation loc ntn (terms,termlists as subst) =
+  if termlists <> [] then CPatNotation (loc,ntn,subst) else
   make_notation_gen loc ntn
-    (fun (loc,ntn,l) -> CPatNotation (loc,ntn,l))
+    (fun (loc,ntn,l) -> CPatNotation (loc,ntn,(l,[])))
     (fun (loc,p) -> CPatPrim (loc,p))
-    destPatPrim l
+    destPatPrim terms
 
  (* Better to use extern_rawconstr composed with injection/retraction ?? *)
 let rec extern_cases_pattern_in_scope (scopes:local_scopes) vars pat =
@@ -834,7 +837,7 @@ and extern_symbol (tmp_scope,scopes as allscopes) vars t = function
           | _, None -> t, [], [], []
           | _ -> raise No_match in
 	(* Try matching ... *)
-	let subst,substlist = match_aconstr t pat in
+	let terms,termlists,binders = match_aconstr t pat in
 	(* Try availability of interpretation ... *)
         let e =
           match keyrule with
@@ -849,17 +852,21 @@ and extern_symbol (tmp_scope,scopes as allscopes) vars t = function
 		    List.map (fun (c,(scopt,scl)) ->
 		      extern (* assuming no overloading: *) true
 		        (scopt,scl@scopes') vars c)
-                      subst in
+                      terms in
 		  let ll =
 		    List.map (fun (c,(scopt,scl)) ->
 		      List.map (extern true (scopt,scl@scopes') vars) c)
-                      substlist in
-	          insert_delimiters (make_notation loc ntn (l,ll)) key)
+                      termlists in
+		  let bll =
+		    List.map (fun (bl,(scopt,scl)) ->
+		      snd (extern_local_binder (scopt,scl@scopes') vars bl))
+                      binders in
+	          insert_delimiters (make_notation loc ntn (l,ll,bll)) key)
           | SynDefRule kn ->
 	      let l =
 		List.map (fun (c,(scopt,scl)) ->
 		  extern true (scopt,scl@scopes) vars c, None)
-		  subst in
+		  terms in
               let a = CRef (Qualid (loc, shortest_qualid_of_syndef vars kn)) in
 	      if l = [] then a else CApp (loc,(None,a),l) in
  	if args = [] then e
diff --git a/interp/constrintern.ml b/interp/constrintern.ml
index 84327add6..25d13bc09 100644
--- a/interp/constrintern.ml
+++ b/interp/constrintern.ml
@@ -206,18 +206,18 @@ let expand_notation_string ntn n =
 
 (* This contracts the special case of "{ _ }" for sumbool, sumor notations *)
 (* Remark: expansion of squash at definition is done in metasyntax.ml *)
-let contract_notation ntn (l,ll) =
+let contract_notation ntn (l,ll,bll) =
   let ntn' = ref ntn in
   let rec contract_squash n = function
     | [] -> []
-    | CNotation (_,"{ _ }",([a],[])) :: l ->
+    | CNotation (_,"{ _ }",([a],[],[])) :: l ->
         ntn' := expand_notation_string !ntn' n;
         contract_squash n (a::l)
     | a :: l ->
         a::contract_squash (n+1) l in
   let l = contract_squash 0 l in
   (* side effect; don't inline *)
-  !ntn',(l,ll)
+  !ntn',(l,ll,bll)
 
 let contract_pat_notation ntn (l,ll) =
   let ntn' = ref ntn in
@@ -240,23 +240,65 @@ let make_current_scope = function
   | (Some tmp_scope,scopes) -> tmp_scope::scopes
   | None,scopes -> scopes
 
-let set_var_scope loc id (_,_,scopt,scopes) varscopes =
-  let idscopes = List.assoc id varscopes in
-  if !idscopes <> None &
-    make_current_scope (Option.get !idscopes)
-    <> make_current_scope (scopt,scopes) then
-      let pr_scope_stack = function
-	| [] -> str "the empty scope stack"
-	| [a] -> str "scope " ++ str a
-	| l -> str "scope stack " ++
-	    str "[" ++ prlist_with_sep pr_comma str l ++ str "]" in
-      user_err_loc (loc,"set_var_scope",
-      pr_id id ++ str " is used both in " ++ 
-	pr_scope_stack (make_current_scope (Option.get !idscopes)) ++
-	strbrk " and in " ++
-	pr_scope_stack (make_current_scope (scopt,scopes)))
-  else
-    idscopes := Some (scopt,scopes)
+let pr_scope_stack = function
+  | [] -> str "the empty scope stack"
+  | [a] -> str "scope " ++ str a
+  | l -> str "scope stack " ++
+      str "[" ++ prlist_with_sep pr_comma str l ++ str "]"
+
+let error_inconsistent_scope loc id scopes1 scopes2 =
+  user_err_loc (loc,"set_var_scope",
+    pr_id id ++ str " is used both in " ++
+    pr_scope_stack scopes1 ++ strbrk " and in " ++ pr_scope_stack scopes2)
+
+let error_expect_constr_notation_type loc id =
+  user_err_loc (loc,"",
+    pr_id id ++ str " is bound in the notation to a term variable.")
+
+let error_expect_binder_notation_type loc id =
+  user_err_loc (loc,"",
+    pr_id id ++
+    str " is expected to occur in binding position in the right-hand side.")
+
+let set_var_scope loc id istermvar (_,_,scopt,scopes) ntnvars =
+  try
+    let idscopes,typ = List.assoc id ntnvars in
+    if !idscopes <> None &
+      make_current_scope (Option.get !idscopes)
+      <> make_current_scope (scopt,scopes) then
+	error_inconsistent_scope loc id
+	  (make_current_scope (Option.get !idscopes))
+	  (make_current_scope (scopt,scopes))
+    else
+      idscopes := Some (scopt,scopes);
+    match typ with
+    | NtnInternTypeBinder ->
+	if istermvar then error_expect_binder_notation_type loc id
+    | NtnInternTypeConstr ->
+	(* We need sometimes to parse idents at a constr level for
+	   factorization and we cannot enforce this constraint:
+	   if not istermvar then error_expect_constr_notation_type loc id *)
+	()
+    | NtnInternTypeIdent -> ()
+  with Not_found ->
+    (* Not in a notation *)
+    ()
+
+let set_type_scope (ids,unb,tmp_scope,scopes) =
+  (ids,unb,Some Notation.type_scope,scopes)
+
+let reset_tmp_scope (ids,unb,tmp_scope,scopes) =
+  (ids,unb,None,scopes)
+
+let rec it_mkRProd env body =
+  match env with
+      (na, bk, _, t) :: tl -> it_mkRProd tl (RProd (dummy_loc, na, bk, t, body))
+    | [] -> body
+
+let rec it_mkRLambda env body =
+  match env with
+      (na, bk, _, t) :: tl -> it_mkRLambda tl (RLambda (dummy_loc, na, bk, t, body))
+    | [] -> body
 
 (**********************************************************************)
 (* Utilities for binders                                              *)
@@ -291,6 +333,7 @@ let push_name_env ?(global_level=false) lvar (ids,unb,tmpsc,scopes as env) =
       env
   | loc,Name id ->
       check_hidden_implicit_parameters id lvar;
+      set_var_scope loc id false env (let (_,_,ntnvars,_) = lvar in ntnvars);
       if global_level then Dumpglob.dump_definition (loc,id) true "var"
       else Dumpglob.dump_binding loc id;
       (Idset.add id ids,unb,tmpsc,scopes)
@@ -325,7 +368,7 @@ let intern_local_binder_aux ?(global_level=false) intern intern_type lvar (env,b
   | LocalRawAssum(nal,bk,ty) ->
       (match bk with
       | Default k ->
-          let (loc,na) = (List.hd nal) in
+          let (loc,na) = List.hd nal in
 	  (* TODO: fail if several names with different implicit types *)
 	  let ty = locate_if_isevar loc na (intern_type env ty) in
 	    List.fold_left
@@ -363,25 +406,53 @@ let intern_generalization intern (ids,unb,tmp_scope,scopes as env) lvar loc bk a
 	  (env', abs lid acc)) fvs (env,c)
   in c'
 
+let iterate_binder intern lvar (env,bl) = function
+  | LocalRawAssum(nal,bk,ty) ->
+      let intern_type env = intern (set_type_scope env) in
+      (match bk with
+      | Default k ->
+          let (loc,na) = List.hd nal in
+	  (* TODO: fail if several names with different implicit types *)
+	  let ty = intern_type env ty in
+	  let ty = locate_if_isevar loc na ty in
+	  List.fold_left
+	    (fun (env,bl) na -> (push_name_env lvar env na,(snd na,k,None,ty)::bl))
+	    (env,bl) nal
+      | Generalized (b,b',t) ->
+	  let env, b = intern_generalized_binder intern_type lvar env bl (List.hd nal) b b' t ty in
+	    env, b @ bl)
+  | LocalRawDef((loc,na as locna),def) ->
+      (push_name_env lvar env locna,
+      (na,Explicit,Some(intern env def),RHole(loc,Evd.BinderType na))::bl)
+
 (**********************************************************************)
 (* Syntax extensions                                                  *)
 
-let traverse_binder (subst,substlist) (renaming,(ids,unb,tmpsc,scopes as env))=
+let option_mem_assoc id = function
+  | Some (id',c) -> id = id'
+  | None -> false
+
+let find_fresh_name renaming (terms,termlists,binders) id =
+  let fvs1 = List.map (fun (_,(c,_)) -> free_vars_of_constr_expr c) terms in
+  let fvs2 = List.flatten (List.map (fun (_,(l,_)) -> List.map free_vars_of_constr_expr l) termlists) in
+  let fvs3 = List.map snd renaming in
+  (* TODO binders *)
+  let fvs = List.flatten (List.map Idset.elements (fvs1@fvs2)) @ fvs3 in
+  next_ident_away id fvs
+
+let traverse_binder (terms,_,_ as subst)
+    (renaming,(ids,unb,tmpsc,scopes as env))=
  function
  | Anonymous -> (renaming,env),Anonymous
  | Name id ->
   try
     (* Binders bound in the notation are considered first-order objects *)
-    let _,na = coerce_to_name (fst (List.assoc id subst)) in
+    let _,na = coerce_to_name (fst (List.assoc id terms)) in
     (renaming,(name_fold Idset.add na ids,unb,tmpsc,scopes)), na
   with Not_found ->
     (* Binders not bound in the notation do not capture variables *)
     (* outside the notation (i.e. in the substitution) *)
-    let fvs1 = List.map (fun (_,(c,_)) -> free_vars_of_constr_expr c) subst in
-    let fvs2 = List.flatten (List.map (fun (_,(l,_)) -> List.map free_vars_of_constr_expr l) substlist) in
-    let fvs3 = List.map snd renaming in
-    let fvs = List.flatten (List.map Idset.elements (fvs1@fvs2)) @ fvs3 in
-    let id' = next_ident_away id fvs in
+    let id' = find_fresh_name renaming subst id in
     let renaming' = if id=id' then renaming else (id,id')::renaming in
     (renaming',env), Name id'
 
@@ -389,17 +460,18 @@ let rec subst_iterator y t = function
   | RVar (_,id) as x -> if id = y then t else x
   | x -> map_rawconstr (subst_iterator y t) x
 
-let rec subst_aconstr_in_rawconstr loc interp (subst,substlist as sub) infos c =
-  let (renaming,(ids,unb,_,scopes)) = infos in
-  let subinfos = renaming,(ids,unb,None,scopes) in
-  match c with
-  | AVar id ->
+let subst_aconstr_in_rawconstr loc intern lvar subst infos c =
+  let (terms,termlists,binders) = subst in
+  let rec aux (terms,binderopt as subst') (renaming,(ids,unb,_,scopes as env)) c =
+    let subinfos = renaming,(ids,unb,None,scopes) in
+    match c with
+    | AVar id ->
       begin
 	(* subst remembers the delimiters stack in the interpretation *)
 	(* of the notations *)
 	try
-	  let (a,(scopt,subscopes)) = List.assoc id subst in
-	  interp (ids,unb,scopt,subscopes@scopes) a
+	  let (a,(scopt,subscopes)) = List.assoc id terms in
+	  intern (ids,unb,scopt,subscopes@scopes) a
 	with Not_found ->
 	try
 	  RVar (loc,List.assoc id renaming)
@@ -407,51 +479,64 @@ let rec subst_aconstr_in_rawconstr loc interp (subst,substlist as sub) infos c =
 	  (* Happens for local notation joint with inductive/fixpoint defs *)
 	  RVar (loc,id)
       end
-  | AList (x,_,iter,terminator,lassoc) ->
+    | AList (x,_,iter,terminator,lassoc) ->
       (try
         (* All elements of the list are in scopes (scopt,subscopes) *)
-	let (l,(scopt,subscopes)) = List.assoc x substlist in
-        let termin =
-          subst_aconstr_in_rawconstr loc interp sub subinfos terminator in
+	let (l,(scopt,subscopes)) = List.assoc x termlists in
+        let termin = aux subst' subinfos terminator in
 	List.fold_right (fun a t ->
           subst_iterator ldots_var t
-            (subst_aconstr_in_rawconstr loc interp
-              ((x,(a,(scopt,subscopes)))::subst,substlist) subinfos iter))
+            (aux ((x,(a,(scopt,subscopes)))::terms,binderopt) subinfos iter))
             (if lassoc then List.rev l else l) termin
       with Not_found ->
           anomaly "Inconsistent substitution of recursive notation")
-  | AHole (Evd.BinderType (Name id as na)) ->
+    | AHole (Evd.BinderType (Name id as na)) ->
       let na =
-        try snd (coerce_to_name (fst (List.assoc id subst)))
+        try snd (coerce_to_name (fst (List.assoc id terms)))
         with Not_found -> na in
       RHole (loc,Evd.BinderType na)
-  | t ->
-      rawconstr_of_aconstr_with_binders loc (traverse_binder sub)
-      (subst_aconstr_in_rawconstr loc interp sub) subinfos t
-
-let intern_notation intern (_,_,tmp_scope,scopes as env) loc ntn fullargs =
-  let ntn,(args,argslist as fullargs) = contract_notation ntn fullargs in
-  let (((ids,idsl),c),df) = interp_notation loc ntn (tmp_scope,scopes) in
+    | ABinderList (x,_,iter,terminator) ->
+      (try
+        (* All elements of the list are in scopes (scopt,subscopes) *)
+	let (bl,(scopt,subscopes)) = List.assoc x binders in
+	let env,bl = List.fold_left (iterate_binder intern lvar) (env,[]) bl in
+        let termin = aux subst' (renaming,env) terminator in
+	List.fold_left (fun t binder ->
+          subst_iterator ldots_var t
+	    (aux (terms,Some(x,binder)) subinfos iter))
+	  termin bl
+      with Not_found ->
+          anomaly "Inconsistent substitution of recursive notation")
+    | AProd (Name id, AHole _, c') when option_mem_assoc id binderopt ->
+	let (na,bk,_,t) = snd (Option.get binderopt) in
+	RProd (loc,na,bk,t,aux subst' infos c')
+    | ALambda (Name id,AHole _,c') when option_mem_assoc id binderopt ->
+	let (na,bk,_,t) = snd (Option.get binderopt) in
+	RLambda (loc,na,bk,t,aux subst' infos c')
+    | t ->
+      rawconstr_of_aconstr_with_binders loc (traverse_binder subst)
+	(aux subst') subinfos t
+  in aux (terms,None) infos c
+
+let split_by_type ids =
+  List.fold_right (fun (x,(scl,typ)) (l1,l2,l3) ->
+    match typ with
+    | NtnTypeConstr -> ((x,scl)::l1,l2,l3)
+    | NtnTypeConstrList -> (l1,(x,scl)::l2,l3)
+    | NtnTypeBinderList -> (l1,l2,(x,scl)::l3)) ids ([],[],[])
+
+let make_subst ids l = List.map2 (fun (id,scl) a -> (id,(a,scl))) ids l
+
+let intern_notation intern (_,_,tmp_scope,scopes as env) lvar loc ntn fullargs =
+  let ntn,(args,argslist,bll as fullargs) = contract_notation ntn fullargs in
+  let ((ids,c),df) = interp_notation loc ntn (tmp_scope,scopes) in
   Dumpglob.dump_notation_location (ntn_loc loc fullargs ntn) ntn df;
-  let subst = List.map2 (fun (id,scl) a -> (id,(a,scl))) ids args in
-  let substlist = List.map2 (fun (id,scl) a -> (id,(a,scl))) idsl argslist in
-  subst_aconstr_in_rawconstr loc intern (subst,substlist) ([],env) c
-
-let set_type_scope (ids,unb,tmp_scope,scopes) =
-  (ids,unb,Some Notation.type_scope,scopes)
-
-let reset_tmp_scope (ids,unb,tmp_scope,scopes) =
-  (ids,unb,None,scopes)
-
-let rec it_mkRProd env body =
-  match env with
-      (na, bk, _, t) :: tl -> it_mkRProd tl (RProd (dummy_loc, na, bk, t, body))
-    | [] -> body
-
-let rec it_mkRLambda env body =
-  match env with
-      (na, bk, _, t) :: tl -> it_mkRLambda tl (RLambda (dummy_loc, na, bk, t, body))
-    | [] -> body
+  let ids,idsl,idsbl = split_by_type ids in
+  let terms = make_subst ids args in
+  let termlists = make_subst idsl argslist in
+  let binders = make_subst idsbl bll in
+  subst_aconstr_in_rawconstr loc intern lvar
+    (terms,termlists,binders) ([],env) c
 
 (**********************************************************************)
 (* Discriminating between bound variables and global references       *)
@@ -479,7 +564,11 @@ let intern_var (ids,_,_,_ as genv) (ltacvars,namedctxvars,ntnvars,impls) loc id
   (* Is [id] a notation variable *)
   else if List.mem_assoc id ntnvars
   then
-    (set_var_scope loc id genv ntnvars; RVar (loc,id), [], [], [])
+    (set_var_scope loc id true genv ntnvars; RVar (loc,id), [], [], [])
+  (* Is [id] the special variable for recursive notations *)
+  else if ntnvars <> [] && id = ldots_var
+  then
+    RVar (loc,id), [], [], []
   else
   (* Is [id] bound to a free name in ltac (this is an ltac error message) *)
   try
@@ -534,7 +623,7 @@ let intern_reference ref =
     (intern_extended_global_of_qualid (qualid_of_reference ref))
 
 (* Is it a global reference or a syntactic definition? *)
-let intern_qualid loc qid intern env args =
+let intern_qualid loc qid intern env lvar args =
   match intern_extended_global_of_qualid (loc,qid) with
   | TrueGlobal ref ->
       RRef (loc, ref), args
@@ -544,25 +633,25 @@ let intern_qualid loc qid intern env args =
       if List.length args < nids then error_not_enough_arguments loc;
       let args1,args2 = list_chop nids args in
       check_no_explicitation args1;
-      let subst = List.map2 (fun (id,scl) a -> (id,(fst a,scl))) ids args1 in
-      subst_aconstr_in_rawconstr loc intern (subst,[]) ([],env) c, args2
+      let subst = make_subst ids (List.map fst args1) in
+      subst_aconstr_in_rawconstr loc intern lvar (subst,[],[]) ([],env) c, args2
 
 (* Rule out section vars since these should have been found by intern_var *)
-let intern_non_secvar_qualid loc qid intern env args =
-  match intern_qualid loc qid intern env args with
+let intern_non_secvar_qualid loc qid intern env lvar args =
+  match intern_qualid loc qid intern env lvar args with
     | RRef (loc, VarRef id),_ -> error_global_not_found_loc loc qid
     | r -> r
 
 let intern_applied_reference intern (_, unb, _, _ as env) lvar args = function
   | Qualid (loc, qid) ->
-      let r,args2 = intern_qualid loc qid intern env args in
+      let r,args2 = intern_qualid loc qid intern env lvar args in
       find_appl_head_data r, args2
   | Ident (loc, id) ->
       try intern_var env lvar loc id, args
       with Not_found ->
       let qid = qualid_of_ident id in
       try
-	let r,args2 = intern_non_secvar_qualid loc qid intern env args in
+	let r,args2 = intern_non_secvar_qualid loc qid intern env lvar args in
 	find_appl_head_data r, args2
       with e ->
 	(* Extra allowance for non globalizing functions *)
@@ -904,7 +993,8 @@ let rec intern_cases_pattern genv scopes (ids,asubst as aliases) tmp_scope pat=
       intern_pat scopes aliases tmp_scope a
   | CPatNotation (loc, ntn, fullargs) ->
       let ntn,(args,argsl as fullargs) = contract_pat_notation ntn fullargs in
-      let (((ids',idsl'),c),df) = Notation.interp_notation loc ntn (tmp_scope,scopes) in
+      let ((ids',c),df) = Notation.interp_notation loc ntn (tmp_scope,scopes) in
+      let (ids',idsl',_) = split_by_type ids' in
       Dumpglob.dump_notation_location (patntn_loc loc fullargs ntn) ntn df;
       let subst = List.map2 (fun (id,scl) a -> (id,(a,scl))) ids' args in
       let substlist = List.map2 (fun (id,scl) a -> (id,(a,scl))) idsl' argsl in
@@ -1090,12 +1180,12 @@ let internalize sigma globalenv env allow_patvar lvar c =
     | CLetIn (loc,na,c1,c2) ->
 	RLetIn (loc, snd na, intern (reset_tmp_scope env) c1,
           intern (push_name_env lvar env na) c2)
-    | CNotation (loc,"- _",([CPrim (_,Numeral p)],[]))
+    | CNotation (loc,"- _",([CPrim (_,Numeral p)],[],[]))
 	when Bigint.is_strictly_pos p ->
 	intern env (CPrim (loc,Numeral (Bigint.neg p)))
-    | CNotation (_,"( _ )",([a],[])) -> intern env a
+    | CNotation (_,"( _ )",([a],[],[])) -> intern env a
     | CNotation (loc,ntn,args) ->
-        intern_notation intern env loc ntn args
+        intern_notation intern env lvar loc ntn args
     | CGeneralization (loc,b,a,c) ->
         intern_generalization intern env lvar loc b a c
     | CPrim (loc, p) ->
@@ -1118,8 +1208,8 @@ let internalize sigma globalenv env allow_patvar lvar c =
 	let (c,impargs,args_scopes,l),args =
           match f with
             | CRef ref -> intern_applied_reference intern env lvar args ref
-            | CNotation (loc,ntn,([],[])) ->
-                let c = intern_notation intern env loc ntn ([],[]) in
+            | CNotation (loc,ntn,([],[],[])) ->
+                let c = intern_notation intern env lvar loc ntn ([],[],[]) in
                 find_appl_head_data c, args
             | x -> (intern env f,[],[],[]), args in
 	let args =
@@ -1260,8 +1350,7 @@ let internalize sigma globalenv env allow_patvar lvar c =
       match bk with
 	| Default b -> default env b nal
 	| Generalized (b,b',t) ->
-	    let env, ibind = intern_generalized_binder intern_type lvar
-	      env [] (List.hd nal) b b' t ty in
+	    let env, ibind = intern_generalized_binder intern_type lvar env [] (List.hd nal) b b' t ty in
 	    let body = intern_type env body in
 	      it_mkRProd ibind body
 
@@ -1276,8 +1365,7 @@ let internalize sigma globalenv env allow_patvar lvar c =
     in match bk with
       | Default b -> default env b nal
       | Generalized (b, b', t) ->
-	  let env, ibind = intern_generalized_binder intern_type lvar
-	    env [] (List.hd nal) b b' t ty in
+	  let env, ibind = intern_generalized_binder intern_type lvar env [] (List.hd nal) b b' t ty in
 	  let body = intern env body in
 	    it_mkRLambda ibind body
 
@@ -1440,19 +1528,20 @@ let intern_constr_pattern sigma env ?(as_type=false) ?(ltacvars=([],[])) c =
   let c = intern_gen as_type ~allow_patvar:true ~ltacvars sigma env c in
   pattern_of_rawconstr c
 
-let interp_aconstr ?(impls=[]) (vars,varslist) a =
+let interp_aconstr ?(impls=[]) vars recvars a =
   let env = Global.env () in
   (* [vl] is intended to remember the scope of the free variables of [a] *)
-  let vl = List.map (fun id -> (id,ref None)) (vars@varslist) in
+  let vl = List.map (fun (id,typ) -> (id,(ref None,typ))) vars in
   let c = internalize Evd.empty (Global.env()) (extract_ids env, false, None, [])
     false (([],[]),Environ.named_context env,vl,impls) a in
   (* Translate and check that [c] has all its free variables bound in [vars] *)
-  let a = aconstr_of_rawconstr vars c in
+  let a = aconstr_of_rawconstr vars recvars c in
+  (* Splits variables into those that are binding, bound, or both *)
+  (* binding and bound *)
+  let out_scope = function None -> None,[] | Some (a,l) -> a,l in
+  let vars = List.map (fun (id,(sc,typ)) -> (id,(out_scope !sc,typ))) vl in
   (* Returns [a] and the ordered list of variables with their scopes *)
-  (* Variables occurring in binders have no relevant scope since bound *)
-  let vl = List.map (fun (id,r) ->
-    (id,match !r with None -> None,[] | Some (a,l) -> a,l)) vl in
-  list_chop (List.length vars) vl, a
+  vars, a
 
 (* Interpret binders and contexts  *)
 
diff --git a/interp/constrintern.mli b/interp/constrintern.mli
index e1f1c50b4..642fc25af 100644
--- a/interp/constrintern.mli
+++ b/interp/constrintern.mli
@@ -171,10 +171,14 @@ val construct_reference : named_context -> identifier -> constr
 val global_reference : identifier -> constr
 val global_reference_in_absolute_module : dir_path -> identifier -> constr
 
-(** Interprets into a abbreviatable constr *)
-
+(** Interprets a term as the left-hand side of a notation; the boolean
+    list is a set and this set is [true] for a variable occurring in
+    term position, [false] for a variable occurring in binding
+    position; [true;false] if in both kinds of position *)
 val interp_aconstr : ?impls:internalization_env ->
-  identifier list * identifier list -> constr_expr -> interpretation
+  (identifier * notation_var_internalization_type) list ->
+  (identifier * identifier) list -> constr_expr ->
+  (identifier * (subscopes * notation_var_internalization_type)) list * aconstr
 
 (** Globalization leak for Grammar *)
 val for_grammar : ('a -> 'b) -> 'a -> 'b
diff --git a/interp/implicit_quantifiers.ml b/interp/implicit_quantifiers.ml
index cad48a5a1..7dbffe668 100644
--- a/interp/implicit_quantifiers.ml
+++ b/interp/implicit_quantifiers.ml
@@ -91,7 +91,7 @@ let is_freevar ids env x =
       with _ -> not (is_global x)
   with _ -> true
 
-(* Auxilliary functions for the inference of implicitly quantified variables. *)
+(* Auxiliary functions for the inference of implicitly quantified variables. *)
 
 let ungeneralizable loc id =
   user_err_loc (loc, "Generalization", 
@@ -108,7 +108,7 @@ let free_vars_of_constr_expr c ?(bound=Idset.empty) l =
   in
   let rec aux bdvars l c = match c with
     | CRef (Ident (loc,id)) -> found loc id bdvars l
-    | CNotation (_, "{ _ : _ | _ }", (CRef (Ident (_, id)) :: _, [])) when not (Idset.mem id bdvars) ->
+    | CNotation (_, "{ _ : _ | _ }", (CRef (Ident (_, id)) :: _, [], [])) when not (Idset.mem id bdvars) ->
 	fold_constr_expr_with_binders (fun a l -> Idset.add a l) aux (Idset.add id bdvars) l c
     | c -> fold_constr_expr_with_binders (fun a l -> Idset.add a l) aux bdvars l c
   in aux bound l c
diff --git a/interp/notation.ml b/interp/notation.ml
index 31e242c1f..a94da4331 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -207,7 +207,8 @@ let cases_pattern_key = function
 
 let aconstr_key = function (* Rem: AApp(ARef ref,[]) stands for @ref *)
   | AApp (ARef ref,args) -> RefKey(make_gr ref), Some (List.length args)
-  | AList (_,_,AApp (ARef ref,args),_,_) -> RefKey (make_gr ref), Some (List.length args)
+  | AList (_,_,AApp (ARef ref,args),_,_)
+  | ABinderList (_,_,AApp (ARef ref,args),_) -> RefKey (make_gr ref), Some (List.length args)
   | ARef ref -> RefKey(make_gr ref), None
   | _ -> Oth, None
 
diff --git a/interp/ppextend.ml b/interp/ppextend.ml
index 16d0537b9..3eec1a3ab 100644
--- a/interp/ppextend.ml
+++ b/interp/ppextend.ml
@@ -51,6 +51,7 @@ let ppcmd_of_cut = function
 type unparsing =
   | UnpMetaVar of int * parenRelation
   | UnpListMetaVar of int * parenRelation * unparsing list
+  | UnpBinderListMetaVar of int * bool * unparsing list
   | UnpTerminal of string
   | UnpBox of ppbox * unparsing list
   | UnpCut of ppcut
diff --git a/interp/ppextend.mli b/interp/ppextend.mli
index 99152c045..d5f32dd2a 100644
--- a/interp/ppextend.mli
+++ b/interp/ppextend.mli
@@ -39,6 +39,7 @@ val ppcmd_of_cut : ppcut -> std_ppcmds
 type unparsing =
   | UnpMetaVar of int * parenRelation
   | UnpListMetaVar of int * parenRelation * unparsing list
+  | UnpBinderListMetaVar of int * bool * unparsing list
   | UnpTerminal of string
   | UnpBox of ppbox * unparsing list
   | UnpCut of ppcut
diff --git a/interp/syntax_def.ml b/interp/syntax_def.ml
index 334135eaf..7790e56d5 100644
--- a/interp/syntax_def.ml
+++ b/interp/syntax_def.ml
@@ -74,8 +74,8 @@ type syndef_interpretation = (identifier * subscopes) list * aconstr
 
 (* Coercions to the general format of notation that also supports
    variables bound to list of expressions *)
-let in_pat (ids,ac) = ((ids,[]),ac)
-let out_pat ((ids,idsl),ac) = assert (idsl=[]); (ids,ac)
+let in_pat (ids,ac) = (List.map (fun (id,sc) -> (id,(sc,NtnTypeConstr))) ids,ac)
+let out_pat (ids,ac) = (List.map (fun (id,(sc,typ)) -> (id,sc)) ids,ac)
 
 let declare_syntactic_definition local id onlyparse pat =
   let _ = add_leaf id (in_syntax_constant (local,in_pat pat,onlyparse)) in ()
diff --git a/interp/topconstr.ml b/interp/topconstr.ml
index db6de8fd1..99dd32868 100644
--- a/interp/topconstr.ml
+++ b/interp/topconstr.ml
@@ -34,6 +34,7 @@ type aconstr =
   (* Part only in rawconstr *)
   | ALambda of name * aconstr * aconstr
   | AProd of name * aconstr * aconstr
+  | ABinderList of identifier * identifier * aconstr * aconstr
   | ALetIn of name * aconstr * aconstr
   | ACases of case_style * aconstr option *
       (aconstr * (name * (inductive * int * name list) option)) list *
@@ -48,6 +49,21 @@ type aconstr =
   | APatVar of patvar
   | ACast of aconstr * aconstr cast_type
 
+type scope_name = string
+
+type tmp_scope_name = scope_name
+
+type subscopes = tmp_scope_name option * scope_name list
+
+type notation_var_instance_type =
+  | NtnTypeConstr | NtnTypeConstrList | NtnTypeBinderList
+
+type notation_var_internalization_type =
+  | NtnInternTypeConstr | NtnInternTypeBinder | NtnInternTypeIdent
+
+type interpretation =
+    (identifier * (subscopes * notation_var_instance_type)) list * aconstr
+
 (**********************************************************************)
 (* Re-interpret a notation as a rawconstr, taking care of binders     *)
 
@@ -67,6 +83,16 @@ let rec cases_pattern_fold_map loc g e = function
 
 let rec subst_rawvars l = function
   | RVar (_,id) as r -> (try List.assoc id l with Not_found -> r)
+  | RProd (loc,Name id,bk,t,c) ->
+      let id =
+	try match List.assoc id l with RVar(_,id') -> id' | _ -> id
+	with Not_found -> id in
+      RProd (loc,Name id,bk,subst_rawvars l t,subst_rawvars l c)
+  | RLambda (loc,Name id,bk,t,c) ->
+      let id =
+	try match List.assoc id l with RVar(_,id') -> id' | _ -> id
+	with Not_found -> id in
+      RLambda (loc,Name id,bk,subst_rawvars l t,subst_rawvars l c)
   | r -> map_rawconstr (subst_rawvars l) r (* assume: id is not binding *)
 
 let ldots_var = id_of_string ".."
@@ -80,6 +106,12 @@ let rawconstr_of_aconstr_with_binders loc g f e = function
       let inner = RApp (loc,RVar (loc,ldots_var),[subst_rawvars innerl it]) in
       let outerl = (ldots_var,inner)::(if swap then [x,RVar(loc,y)] else []) in
       subst_rawvars outerl it
+  | ABinderList (x,y,iter,tail) ->
+      let t = f e tail in let it = f e iter in
+      let innerl = [(ldots_var,t);(x,RVar(loc,y))] in
+      let inner = RApp (loc,RVar (loc,ldots_var),[subst_rawvars innerl it]) in
+      let outerl = [(ldots_var,inner)] in
+      subst_rawvars outerl it
   | ALambda (na,ty,c) ->
       let e,na = g e na in RLambda (loc,na,Explicit,f e ty,f e c)
   | AProd (na,ty,c) ->
@@ -132,72 +164,135 @@ let rec rawconstr_of_aconstr loc x =
 (****************************************************************************)
 (* Translating a rawconstr into a notation, interpreting recursive patterns *)
 
-let add_name r = function
-  | Anonymous -> ()
-  | Name id -> r := id :: !r
+let add_id r id = r := (id :: pi1 !r, pi2 !r, pi3 !r)
+let add_name r = function Anonymous -> () | Name id -> add_id r id
 
-let has_ldots =
-  List.exists
-    (function RApp (_,RVar(_,v),_) when v = ldots_var -> true | _ -> false)
-
-let compare_rawconstr f t1 t2 = match t1,t2 with
-  | RRef (_,r1), RRef (_,r2) -> eq_gr r1 r2 
-  | RVar (_,v1), RVar (_,v2) -> v1 = v2
-  | RApp (_,f1,l1), RApp (_,f2,l2) -> f f1 f2 & List.for_all2 f l1 l2
-  | RLambda (_,na1,bk1,ty1,c1), RLambda (_,na2,bk2,ty2,c2) when na1 = na2 && bk1 = bk2 ->
-      f ty1 ty2 & f c1 c2
+let split_at_recursive_part c =
+  let sub = ref None in
+  let rec aux = function
+  | RApp (loc0,RVar(loc,v),c::l) when v = ldots_var ->
+      if !sub <> None then
+	(* Not narrowed enough to find only one recursive part *)
+	raise Not_found
+      else
+	(sub := Some c;
+	 if l = [] then RVar (loc,ldots_var)
+	 else RApp (loc0,RVar (loc,ldots_var),l))
+  | c -> map_rawconstr aux c in
+  let outer_iterator = aux c in
+  match !sub with
+  | None -> (* No recursive pattern found *) raise Not_found
+  | Some c ->
+  match outer_iterator with
+  | RVar (_,v) when v = ldots_var -> (* Not enough context *) raise Not_found
+  | _ -> outer_iterator, c
+
+let on_true_do b f c = if b then (f c; b) else b
+
+let compare_rawconstr f add t1 t2 = match t1,t2 with
+  | RRef (_,r1), RRef (_,r2) -> eq_gr r1 r2
+  | RVar (_,v1), RVar (_,v2) -> on_true_do (v1 = v2) add (Name v1)
+  | RApp (_,f1,l1), RApp (_,f2,l2) -> f f1 f2 & list_for_all2eq f l1 l2
+  | RLambda (_,na1,bk1,ty1,c1), RLambda (_,na2,bk2,ty2,c2) when na1 = na2 && bk1 = bk2 -> on_true_do (f ty1 ty2 & f c1 c2) add na1
   | RProd (_,na1,bk1,ty1,c1), RProd (_,na2,bk2,ty2,c2) when na1 = na2 && bk1 = bk2 ->
-      f ty1 ty2 & f c1 c2
+      on_true_do (f ty1 ty2 & f c1 c2) add na1
   | RHole _, RHole _ -> true
   | RSort (_,s1), RSort (_,s2) -> s1 = s2
-  | (RLetIn _ | RCases _ | RRec _ | RDynamic _
+  | RLetIn (_,na1,b1,c1), RLetIn (_,na2,b2,c2) when na1 = na2 ->
+      on_true_do (f b1 b2 & f c1 c2) add na1
+  | (RCases _ | RRec _ | RDynamic _
     | RPatVar _ | REvar _ | RLetTuple _ | RIf _ | RCast _),_
-  | _,(RLetIn _ | RCases _ | RRec _ | RDynamic _
+  | _,(RCases _ | RRec _ | RDynamic _
       | RPatVar _ | REvar _ | RLetTuple _ | RIf _ | RCast _)
       -> error "Unsupported construction in recursive notations."
-  | (RRef _ | RVar _ | RApp _ | RLambda _ | RProd _ | RHole _ | RSort _), _
+  | (RRef _ | RVar _ | RApp _ | RLambda _ | RProd _
+    | RHole _ | RSort _ | RLetIn _), _
       -> false
 
-let rec eq_rawconstr t1 t2 = compare_rawconstr eq_rawconstr t1 t2
+let rec eq_rawconstr t1 t2 = compare_rawconstr eq_rawconstr (fun _ -> ()) t1 t2
+
+let subtract_loc loc1 loc2 = make_loc (fst (unloc loc1),fst (unloc loc2)-1)
 
-let discriminate_patterns foundvars nl l1 l2 =
+let check_is_hole id = function RHole _ -> () | t ->
+  user_err_loc (loc_of_rawconstr t,"",
+    strbrk "In recursive notation with binders, " ++ pr_id id ++
+    strbrk " is expected to come without type.")
+
+let compare_recursive_parts found f (iterator,subc) =
   let diff = ref None in
-  let rec aux n c1 c2 = match c1,c2 with
-  | RVar (_,v1), RVar (_,v2) when v1<>v2 ->
-      if !diff = None then (diff := Some (v1,v2,(n>=nl)); true)
-      else
-        !diff = Some (v1,v2,(n>=nl)) or !diff = Some (v2,v1,(n<nl))
-        or (error
-          "Both ends of the recursive pattern differ in more than one place")
-  | _ -> compare_rawconstr (aux (n+1)) c1 c2 in
-  let l = list_map2_i aux 0 l1 l2 in
-  if not (List.for_all ((=) true) l) then
-    error "Both ends of the recursive pattern differ.";
-  match !diff with
-    | None ->  error "Both ends of the recursive pattern are the same."
-    | Some (x,y,_ as discr) ->
-	List.iter (fun id ->
-          if List.mem id !foundvars
-          then errorlabstrm "" (strbrk "Variables used in the recursive part of a pattern are not allowed to occur outside of the recursive part.");
-          foundvars := id::!foundvars) [x;y];
-	discr
+  let terminator = ref None in
+  let rec aux c1 c2 = match c1,c2 with
+  | RVar(_,v), term when v = ldots_var ->
+      (* We found the pattern *)
+      assert (!terminator = None); terminator := Some term;
+      true
+  | RApp (_,RVar(_,v),l1), RApp (_,term,l2) when v = ldots_var ->
+      (* We found the pattern, but there are extra arguments *)
+      (* (this allows e.g. alternative (recursive) notation of application) *)
+      assert (!terminator = None); terminator := Some term;
+      list_for_all2eq aux l1 l2
+  | RVar (_,x), RVar (_,y) when x<>y ->
+      (* We found the position where it differs *)
+      let lassoc = (!terminator <> None) in
+      let x,y = if lassoc then y,x else x,y in
+      !diff = None && (diff := Some (x,y,Some lassoc); true)
+  | RLambda (_,Name x,_,t_x,c), RLambda (_,Name y,_,t_y,term)
+  | RProd (_,Name x,_,t_x,c), RProd (_,Name y,_,t_y,term) ->
+      (* We found a binding position where it differs *)
+      check_is_hole y t_x;
+      check_is_hole y t_y;
+      !diff = None && (diff := Some (x,y,None); aux c term)
+  | _ ->
+      compare_rawconstr aux (add_name found) c1 c2 in
+  if aux iterator subc then
+    match !diff with
+    | None ->
+	let loc1 = loc_of_rawconstr iterator in
+	let loc2 = loc_of_rawconstr (Option.get !terminator) in
+	(* Here, we would need a loc made of several parts ... *)
+	user_err_loc (subtract_loc loc1 loc2,"",
+          str "Both ends of the recursive pattern are the same.")
+    | Some (x,y,Some lassoc) ->
+	let newfound = (pi1 !found, (x,y) :: pi2 !found, pi3 !found) in
+	let iterator =
+	  f (if lassoc then subst_rawvars [y,RVar(dummy_loc,x)] iterator
+	  else iterator) in
+	(* found have been collected by compare_constr *)
+	found := newfound;
+	AList (x,y,iterator,f (Option.get !terminator),lassoc)
+    | Some (x,y,None) ->
+	let newfound = (pi1 !found, pi2 !found, (x,y) :: pi3 !found) in
+	let iterator = f iterator in
+	(* found have been collected by compare_constr *)
+	found := newfound;
+	ABinderList (x,y,iterator,f (Option.get !terminator))
+  else
+    raise Not_found
 
 let aconstr_and_vars_of_rawconstr a =
-  let found = ref [] in
-  let rec aux = function
-  | RVar (_,id) -> found := id::!found; AVar id
-  | RApp (_,f,args) when has_ldots args -> make_aconstr_list f args
-  | RApp (_,RVar (_,f),[RApp (_,t,[c]);d]) when f = ldots_var ->
-      (* Special case for alternative (recursive) notation of application *)
-      let x,y,lassoc = discriminate_patterns found 0 [c] [d] in
-      found := ldots_var :: !found; assert lassoc;
-      AList (x,y,AApp (AVar ldots_var,[AVar x]),aux t,lassoc)
+  let found = ref ([],[],[]) in
+  let rec aux c =
+    let keepfound = !found in
+    (* n^2 complexity but small and done only once per notation *)
+    try compare_recursive_parts found aux' (split_at_recursive_part c)
+    with Not_found ->
+    found := keepfound;
+    match c with
+    | RApp (_,RVar (loc,f),[c]) when f = ldots_var ->
+	(* Fall on the second part of the recursive pattern w/o having
+	   found the first part *)
+	user_err_loc (loc,"",
+	str "Cannot find where the recursive pattern starts.")
+    | c ->
+	aux' c
+  and aux' = function
+  | RVar (_,id) -> add_id found id; AVar id
   | RApp (_,g,args) -> AApp (aux g, List.map aux args)
   | RLambda (_,na,bk,ty,c) -> add_name found na; ALambda (na,aux ty,aux c)
   | RProd (_,na,bk,ty,c) -> add_name found na; AProd (na,aux ty,aux c)
   | RLetIn (_,na,b,c) -> add_name found na; ALetIn (na,aux b,aux c)
   | RCases (_,sty,rtntypopt,tml,eqnl) ->
-      let f (_,idl,pat,rhs) = found := idl@(!found); (pat,aux rhs) in
+      let f (_,idl,pat,rhs) = List.iter (add_id found) idl; (pat,aux rhs) in
       ACases (sty,Option.map aux rtntypopt,
         List.map (fun (tm,(na,x)) ->
 	  add_name found na;
@@ -213,7 +308,7 @@ let aconstr_and_vars_of_rawconstr a =
       add_name found na;
       AIf (aux c,(na,Option.map aux po),aux b1,aux b2)
   | RRec (_,fk,idl,dll,tl,bl) ->
-      Array.iter (fun id -> found := id::!found) idl;
+      Array.iter (add_id found) idl;
       let dll = Array.map (List.map (fun (na,bk,oc,b) ->
 	 if bk <> Explicit then
 	   error "Binders marked as implicit not allowed in notations.";
@@ -229,51 +324,61 @@ let aconstr_and_vars_of_rawconstr a =
   | RDynamic _ | REvar _ ->
       error "Existential variables not allowed in notations."
 
-  (* Recognizing recursive notations *)
-  and terminator_of_pat f1 ll1 lr1 = function
-  | RApp (loc,f2,l2) ->
-      if not (eq_rawconstr f1 f2) then errorlabstrm ""
-	(strbrk "Cannot recognize the same head to both ends of the recursive pattern.");
-      let nl = List.length ll1 in
-      let nr = List.length lr1 in
-      if List.length l2 <> nl + nr + 1 then
-	error "Both ends of the recursive pattern have different lengths.";
-      let ll2,l2' = list_chop nl l2 in
-      let t = List.hd l2' and lr2 = List.tl l2' in
-      let x,y,order = discriminate_patterns found nl (ll1@lr1) (ll2@lr2) in
-      let iter =
-        if order then RApp (loc,f2,ll2@RVar (loc,ldots_var)::lr2)
-        else RApp (loc,f1,ll1@RVar (loc,ldots_var)::lr1) in
-      (if order then y else x),(if order then x else y), aux iter, aux t, order
-  | _ -> error "One end of the recursive pattern is not an application."
-
-  and make_aconstr_list f args =
-    let rec find_patterns acc = function
-      | RApp(_,RVar (_,a),[c]) :: l when a = ldots_var ->
-          (* We've found the recursive part *)
-	  let x,y,iter,term,lassoc = terminator_of_pat f (List.rev acc) l c in
-	  AList (x,y,iter,term,lassoc)
-      | a::l -> find_patterns (a::acc) l
-      | [] -> error "Ill-formed recursive notation."
-    in find_patterns [] args
-
   in
   let t = aux a in
   (* Side effect *)
   t, !found
 
-let aconstr_of_rawconstr vars a =
-  let a,foundvars = aconstr_and_vars_of_rawconstr a in
-  let check_type x =
-    if not (List.mem x foundvars) then
-      error ((string_of_id x)^" is unbound in the right-hand-side.") in
-  List.iter check_type vars;
+let rec list_rev_mem_assoc x = function
+  | [] -> false
+  | (_,x')::l -> x = x' || list_rev_mem_assoc x l
+
+let check_variables vars recvars (found,foundrec,foundrecbinding) =
+  let useless_vars = List.map snd recvars in
+  let vars = List.filter (fun (y,_) -> not (List.mem y useless_vars)) vars in
+  let check_recvar x =
+    if List.mem x found then
+      errorlabstrm "" (pr_id x ++
+	strbrk " should only be used in the recursive part of a pattern.") in
+  List.iter (fun (x,y) -> check_recvar x; check_recvar y)
+    (foundrec@foundrecbinding);
+  let check_bound x =
+    if not (List.mem x found) then
+      if List.mem_assoc x foundrec or List.mem_assoc x foundrecbinding
+	or list_rev_mem_assoc x foundrec or list_rev_mem_assoc x foundrecbinding
+      then
+	error ((string_of_id x)^" should not be bound in a recursive pattern of the right-hand side.")
+      else
+	error ((string_of_id x)^" is unbound in the right-hand side.") in
+  let check_pair s x y where =
+    if not (List.mem (x,y) where) then
+      errorlabstrm "" (strbrk "in the right-hand side, " ++ pr_id x ++
+	str " and " ++ pr_id y ++ strbrk " should appear in " ++ str s ++
+	str " position as part of a recursive pattern.") in
+  let check_type (x,typ) =
+    match typ with
+    | NtnInternTypeConstr ->
+	begin
+	  try check_pair "term" x (List.assoc x recvars) foundrec
+	  with Not_found -> check_bound x
+	end
+    | NtnInternTypeBinder ->
+	begin
+	  try check_pair "binding" x (List.assoc x recvars) foundrecbinding
+	  with Not_found -> check_bound x
+	end
+    | NtnInternTypeIdent -> check_bound x in
+  List.iter check_type vars
+
+let aconstr_of_rawconstr vars recvars a =
+  let a,found = aconstr_and_vars_of_rawconstr a in
+  check_variables vars recvars found;
   a
 
 (* Substitution of kernel names, avoiding a list of bound identifiers *)
 
 let aconstr_of_constr avoiding t =
- aconstr_of_rawconstr [] (Detyping.detype false avoiding [] t)
+ aconstr_of_rawconstr [] [] (Detyping.detype false avoiding [] t)
 
 let rec subst_pat subst pat =
   match pat with
@@ -317,6 +422,12 @@ let rec subst_aconstr subst bound raw =
 	if r1' == r1 && r2' == r2 then raw else
 	  AProd (n,r1',r2')
 
+  | ABinderList (id1,id2,r1,r2) ->
+      let r1' = subst_aconstr subst bound r1
+      and r2' = subst_aconstr subst bound r2 in
+	if r1' == r1 && r2' == r2 then raw else
+	  ABinderList (id1,id2,r1',r2')
+
   | ALetIn (n,r1,r2) ->
       let r1' = subst_aconstr subst bound r1
       and r2' = subst_aconstr subst bound r2 in
@@ -394,7 +505,7 @@ let rec subst_aconstr subst bound raw =
 		ACast (r1',CastCoerce)
 
 let subst_interpretation subst (metas,pat) =
-  let bound = List.map fst (fst metas @ snd metas) in
+  let bound = List.map fst metas in
   (metas,subst_aconstr subst bound pat)
 
 let encode_list_value l = RApp (dummy_loc,RVar (dummy_loc,ldots_var),l)
@@ -432,7 +543,7 @@ let rec alpha_var id1 id2 = function
 
 let alpha_eq_val (x,y) = x = y
 
-let bind_env alp (sigma,sigmalist as fullsigma) var v =
+let bind_env alp (sigma,sigmalist,sigmabinders as fullsigma) var v =
   try
     let vvar = List.assoc var sigma in
     if alpha_eq_val (v,vvar) then fullsigma
@@ -441,7 +552,10 @@ let bind_env alp (sigma,sigmalist as fullsigma) var v =
     (* Check that no capture of binding variables occur *)
     if List.exists (fun (id,_) ->occur_rawconstr id v) alp then raise No_match;
     (* TODO: handle the case of multiple occs in different scopes *)
-    ((var,v)::sigma,sigmalist)
+    ((var,v)::sigma,sigmalist,sigmabinders)
+
+let bind_binder (sigma,sigmalist,sigmabinders) x bl =
+  (sigma,sigmalist,(x,List.rev bl)::sigmabinders)
 
 let match_fix_kind fk1 fk2 =
   match (fk1,fk2) with
@@ -456,13 +570,9 @@ let match_opt f sigma t1 t2 = match (t1,t2) with
   | Some t1, Some t2 -> f sigma t1 t2
   | _ -> raise No_match
 
-let rawconstr_of_name = function
-  | Anonymous -> RHole (dummy_loc,Evd.InternalHole)
-  | Name id -> RVar (dummy_loc,id)
-
 let match_names metas (alp,sigma) na1 na2 = match (na1,na2) with
-  | (na,Name id2) when List.mem id2 metas ->
-      alp, bind_env alp sigma id2 (rawconstr_of_name na)
+  | (Name id1,Name id2) when List.mem id2 metas ->
+      alp, bind_env alp sigma id2 (RVar (dummy_loc,id1))
   | (Name id1,Name id2) -> (id1,id2)::alp,sigma
   | (Anonymous,Anonymous) -> alp,sigma
   | _ -> raise No_match
@@ -480,33 +590,80 @@ let adjust_application_n n loc f l =
   let l1,l2 = list_chop (List.length l - n) l in
   if l1 = [] then f,l else RApp (loc,f,l1), l2
 
-let match_alist match_fun metas sigma l1 l2 x iter termin lassoc =
-  (* match the iterator at least once *)
-  let sigmavar,sigmalist =
-    List.fold_left2 (match_fun (ldots_var::metas)) sigma l1 l2 in
-  (* Recover the recursive position *)
-  let rest = List.assoc ldots_var sigmavar in
-  (* Recover the first element *)
-  let t1 = List.assoc x sigmavar in
-  let sigmavar = List.remove_assoc x (List.remove_assoc ldots_var sigmavar) in
-  (* try to find the remaining elements or the terminator *)
-  let rec match_alist_tail metas sigma acc rest =
+let glue_letin_with_decls = true
+
+let rec match_iterated_binders islambda decls = function
+  | RLambda (_,na,bk,t,b) when islambda ->
+      match_iterated_binders islambda ((na,bk,None,t)::decls) b
+  | RProd (_,(Name _ as na),bk,t,b) when not islambda ->
+      match_iterated_binders islambda ((na,bk,None,t)::decls) b
+  | RLetIn (loc,na,c,b) when glue_letin_with_decls ->
+      match_iterated_binders islambda
+	((na,Explicit (*?*), Some c,RHole(loc,Evd.BinderType na))::decls) b
+  | b -> (decls,b)
+
+let remove_sigma x (sigmavar,sigmalist,sigmabinders) =
+  (List.remove_assoc x sigmavar,sigmalist,sigmabinders)
+
+let rec match_abinderlist_with_app match_fun metas sigma rest x iter termin =
+  let rec aux sigma acc rest =
     try
-      let sigmavar,sigmalist = match_fun (ldots_var::metas) sigma rest iter in
-      let rest = List.assoc ldots_var sigmavar in
-      let t = List.assoc x sigmavar in
-      let sigmavar =
-	List.remove_assoc x (List.remove_assoc ldots_var sigmavar) in
-      match_alist_tail metas (sigmavar,sigmalist) (t::acc) rest
-    with No_match ->
-      List.rev acc, match_fun metas (sigmavar,sigmalist) rest termin in
-  let tl,(sigmavar,sigmalist) = match_alist_tail metas sigma [t1] rest in
-  (sigmavar, (x,if lassoc then List.rev tl else tl)::sigmalist)
+      let sigma = match_fun (ldots_var::metas) sigma rest iter in
+      let rest = List.assoc ldots_var (pi1 sigma) in
+      let b = match List.assoc x (pi3 sigma) with [b] -> b | _ ->assert false in
+      let sigma = remove_sigma x (remove_sigma ldots_var sigma) in
+      aux sigma (b::acc) rest
+    with No_match when acc <> [] ->
+      acc, match_fun metas sigma rest termin in
+  let bl,sigma = aux sigma [] rest in
+  bind_binder sigma x bl
+
+let match_alist match_fun metas sigma rest x iter termin lassoc =
+  let rec aux sigma acc rest =
+    try
+      let sigma = match_fun (ldots_var::metas) sigma rest iter in
+      let rest = List.assoc ldots_var (pi1 sigma) in
+      let t = List.assoc x (pi1 sigma) in
+      let sigma = remove_sigma x (remove_sigma ldots_var sigma) in
+      aux sigma (t::acc) rest
+    with No_match when acc <> [] ->
+      acc, match_fun metas sigma rest termin in
+  let l,sigma = aux sigma [] rest in
+  (pi1 sigma, (x,if lassoc then l else List.rev l)::pi2 sigma, pi3 sigma)
 
 let rec match_ alp metas sigma a1 a2 = match (a1,a2) with
+
+  (* Matching notation variable *)
   | r1, AVar id2 when List.mem id2 metas -> bind_env alp sigma id2 r1
+
+  (* Matching recursive notations for terms *)
+  | r1, AList (x,_,iter,termin,lassoc) ->
+      match_alist (match_ alp) metas sigma r1 x iter termin lassoc
+
+  (* Matching recursive notations for binders: ad hoc cases supporting let-in *)
+  | RLambda (_,na1,bk,t1,b1), ABinderList (x,_,ALambda (Name id2,_,b2),termin)->
+      let (decls,b) = match_iterated_binders true [(na1,bk,None,t1)] b1 in
+      (* TODO: address the possibility that termin is a Lambda itself *)
+      match_ alp metas (bind_binder sigma x decls) b termin
+  | RProd (_,na1,bk,t1,b1), ABinderList (x,_,AProd (Name id2,_,b2),termin)
+      when na1 <> Anonymous ->
+      let (decls,b) = match_iterated_binders false [(na1,bk,None,t1)] b1 in
+      (* TODO: address the possibility that termin is a Prod itself *)
+      match_ alp metas (bind_binder sigma x decls) b termin
+  (* Matching recursive notations for binders: general case *)
+  | r, ABinderList (x,_,iter,termin) ->
+      match_abinderlist_with_app (match_ alp) metas sigma r x iter termin
+
+  (* Matching individual binders *)
+  | RLambda (_,na,bk,t,b1), ALambda (Name id,_,b2) when List.mem id metas ->
+      match_ alp metas (bind_binder sigma id [(na,bk,None,t)]) b1 b2
+  | RProd (_,na,bk,t,b1), AProd (Name id,_,b2)
+      when List.mem id metas & na <> Anonymous ->
+      match_ alp metas (bind_binder sigma id [(na,bk,None,t)]) b1 b2
+
+  (* Matching compositionally *)
   | RVar (_,id1), AVar id2 when alpha_var id1 id2 alp -> sigma
-  | RRef (_,r1), ARef r2 when (eq_gr r1 r2) -> sigma 
+  | RRef (_,r1), ARef r2 when (eq_gr r1 r2) -> sigma
   | RPatVar (_,(_,n1)), APatVar n2 when n1=n2 -> sigma
   | RApp (loc,f1,l1), AApp (f2,l2) ->
       let n1 = List.length l1 and n2 = List.length l2 in
@@ -517,11 +674,6 @@ let rec match_ alp metas sigma a1 a2 = match (a1,a2) with
 	  let l11,l12 = list_chop (n1-n2) l1 in RApp (loc,f1,l11),l12, f2,l2
 	else f1,l1, f2, l2 in
       List.fold_left2 (match_ alp metas) (match_ alp metas sigma f1 f2) l1 l2
-  | RApp (loc,f1,l1), AList (x,_,(AApp (f2,l2) as iter),termin,lassoc)
-      when List.length l1 >= List.length l2 ->
-      let f1,l1 = adjust_application_n (List.length l2) loc f1 l1 in
-      match_alist (match_ alp)
-	metas sigma (f1::l1) (f2::l2) x iter termin lassoc
   | RLambda (_,na1,_,t1,b1), ALambda (na2,t2,b2) ->
      match_binders alp metas na1 na2 (match_ alp metas sigma t1 t2) b1 b2
   | RProd (_,na1,_,t1,b1), AProd (na2,t2,b2) ->
@@ -586,38 +738,35 @@ and match_equations alp metas sigma (_,_,patl1,rhs1) (patl2,rhs2) =
       (alp,sigma) patl1 patl2 in
   match_ alp metas sigma rhs1 rhs2
 
-type scope_name = string
-
-type tmp_scope_name = scope_name
-
-type subscopes = tmp_scope_name option * scope_name list
-
-type interpretation =
-    (* regular vars of notation    / recursive parts of notation    / body *)
-    ((identifier * subscopes) list * (identifier * subscopes) list) * aconstr
-
-let match_aconstr c ((metas_scl,metaslist_scl),pat) =
-  let vars = List.map fst metas_scl @ List.map fst metaslist_scl in
-  let subst,substlist = match_ [] vars ([],[]) c pat in
+let match_aconstr c (metas,pat) =
+  let vars = List.map fst metas in
+  let terms,termlists,binders = match_ [] vars ([],[],[]) c pat in
   (* Reorder canonically the substitution *)
   let find x =
-    try List.assoc x subst
+    try List.assoc x terms
     with Not_found ->
       (* Happens for binders bound to Anonymous *)
       (* Find a better way to propagate Anonymous... *)
       RVar (dummy_loc,x) in
-  List.map (fun (x,scl) -> (find x,scl)) metas_scl,
-  List.map (fun (x,scl) -> (List.assoc x substlist,scl)) metaslist_scl
+  List.fold_right (fun (x,(scl,typ)) (terms',termlists',binders') ->
+    match typ with
+    | NtnTypeConstr ->
+       ((find x, scl)::terms',termlists',binders')
+    | NtnTypeConstrList ->
+       (terms',(List.assoc x termlists,scl)::termlists',binders')
+    | NtnTypeBinderList ->
+       (terms',termlists',(List.assoc x binders,scl)::binders'))
+    metas ([],[],[])
 
 (* Matching cases pattern *)
 
-let bind_env_cases_pattern (sigma,sigmalist as fullsigma) var v =
+let bind_env_cases_pattern (sigma,sigmalist,x as fullsigma) var v =
   try
     let vvar = List.assoc var sigma in
     if v=vvar then fullsigma else raise No_match
   with Not_found ->
     (* TODO: handle the case of multiple occs in different scopes *)
-    (var,v)::sigma,sigmalist
+    (var,v)::sigma,sigmalist,x
 
 let rec match_cases_pattern metas sigma a1 a2 = match (a1,a2) with
   | r1, AVar id2 when List.mem id2 metas -> bind_env_cases_pattern sigma id2 r1
@@ -637,26 +786,33 @@ let rec match_cases_pattern metas sigma a1 a2 = match (a1,a2) with
         (* All parameters must be _ *)
         List.iter (function AHole _ -> () | _ -> raise No_match) p2;
 	List.fold_left2 (match_cases_pattern metas) sigma args1 args2
+  | r1, AList (x,_,iter,termin,lassoc) ->
+      match_alist match_cases_pattern
+	metas (pi1 sigma,pi2 sigma,()) r1 x iter termin lassoc
+(*
   | PatCstr (loc,(ind,_ as r1),args1,_),
-    AList (x,_,(AApp (ARef (ConstructRef r2),l2) as iter),termin,lassoc)
+    AList (x,y,(AApp (ARef (ConstructRef r2),l2) as iter),termin,lassoc)
       when r1 = r2 ->
       let nparams = Inductive.inductive_params (Global.lookup_inductive ind) in
       assert (List.length args1 + nparams = List.length l2);
       let (p2,args2) = list_chop nparams l2 in
       List.iter (function AHole _ -> () | _ -> raise No_match) p2;
+      let x = if lassoc then x else y in
       match_alist match_cases_pattern
-	metas sigma args1 args2 x iter termin lassoc
+	metas (pi1 sigma,pi2 sigma,()) args1 args2 x iter termin lassoc
+*)
   | _ -> raise No_match
 
-let match_aconstr_cases_pattern c ((metas_scl,metaslist_scl),pat) =
-  let vars = List.map fst metas_scl @ List.map fst metaslist_scl in
-  let subst,substlist = match_cases_pattern vars ([],[]) c pat in
+let match_aconstr_cases_pattern c (metas,pat) =
+  let vars = List.map fst metas in
+  let terms,termlists,() = match_cases_pattern vars ([],[],()) c pat in
   (* Reorder canonically the substitution *)
-  let find x subst =
-    try List.assoc x subst
-    with Not_found -> anomaly "match_aconstr_cases_pattern" in
-  List.map (fun (x,scl) -> (find x subst,scl)) metas_scl,
-  List.map (fun (x,scl) -> (find x substlist,scl)) metaslist_scl
+  List.fold_right (fun (x,(scl,typ)) (terms',termlists') ->
+    match typ with
+    | NtnTypeConstr -> ((List.assoc x terms, scl)::terms',termlists')
+    | NtnTypeConstrList -> (terms',(List.assoc x termlists,scl)::termlists')
+    | NtnTypeBinderList -> assert false)
+    metas ([],[])
 
 (**********************************************************************)
 (*s Concrete syntax for terms *)
@@ -673,19 +829,20 @@ type proj_flag = int option (* [Some n] = proj of the n-th visible argument *)
 
 type prim_token = Numeral of Bigint.bigint | String of string
 
-type 'a notation_substitution =
-    'a list * (* for recursive notations: *) 'a list list
-
 type cases_pattern_expr =
   | CPatAlias of loc * cases_pattern_expr * identifier
   | CPatCstr of loc * reference * cases_pattern_expr list
   | CPatAtom of loc * reference option
   | CPatOr of loc * cases_pattern_expr list
-  | CPatNotation of loc * notation * cases_pattern_expr notation_substitution
+  | CPatNotation of loc * notation * cases_pattern_notation_substitution
   | CPatPrim of loc * prim_token
-  | CPatRecord of loc * (reference * cases_pattern_expr) list
+  | CPatRecord of Util.loc * (reference * cases_pattern_expr) list
   | CPatDelimiters of loc * string * cases_pattern_expr
 
+and cases_pattern_notation_substitution =
+    cases_pattern_expr list *     (** for constr subterms *)
+    cases_pattern_expr list list  (** for recursive notations *)
+
 type constr_expr =
   | CRef of reference
   | CFix of loc * identifier located * fix_expr list
@@ -710,7 +867,7 @@ type constr_expr =
   | CEvar of loc * existential_key * constr_expr list option
   | CSort of loc * rawsort
   | CCast of loc * constr_expr * constr_expr cast_type
-  | CNotation of loc * notation * constr_expr notation_substitution
+  | CNotation of loc * notation * constr_notation_substitution
   | CGeneralization of loc * binding_kind * abstraction_kind option * constr_expr
   | CPrim of loc * prim_token
   | CDelimiters of loc * string * constr_expr
@@ -719,14 +876,6 @@ type constr_expr =
 and fix_expr =
     identifier located * (identifier located option * recursion_order_expr) * local_binder list * constr_expr * constr_expr
 
-and local_binder =
-  | LocalRawDef of name located * constr_expr
-  | LocalRawAssum of name located list * binder_kind * constr_expr
-
-and typeclass_constraint = name located * binding_kind * constr_expr
-
-and typeclass_context = typeclass_constraint list
-
 and cofix_expr =
     identifier located * local_binder list * constr_expr * constr_expr
 
@@ -735,6 +884,19 @@ and recursion_order_expr =
   | CWfRec of constr_expr
   | CMeasureRec of constr_expr * constr_expr option (* measure, relation *)
 
+and local_binder =
+  | LocalRawDef of name located * constr_expr
+  | LocalRawAssum of name located list * binder_kind * constr_expr
+
+and constr_notation_substitution =
+    constr_expr list *      (* for constr subterms *)
+    constr_expr list list * (* for recursive notations *)
+    local_binder list list      (* for binders subexpressions *)
+
+type typeclass_constraint = name located * binding_kind * constr_expr
+
+and typeclass_context = typeclass_constraint list
+
 type constr_pattern_expr = constr_expr
 
 (***********************)
@@ -787,6 +949,15 @@ let cases_pattern_expr_loc = function
   | CPatPrim (loc,_) -> loc
   | CPatDelimiters (loc,_,_) -> loc
 
+let local_binder_loc = function
+  | LocalRawAssum ((loc,_)::_,_,t)
+  | LocalRawDef ((loc,_),t) -> join_loc loc (constr_loc t)
+  | LocalRawAssum ([],_,_) -> assert false
+
+let local_binders_loc bll =
+  if bll = [] then dummy_loc else
+  join_loc (local_binder_loc (List.hd bll)) (local_binder_loc (list_last bll))
+
 let occur_var_constr_ref id = function
   | Ident (loc,id') -> id = id'
   | Qualid _ -> false
@@ -796,7 +967,7 @@ let ids_of_cases_indtype =
   let rec vars_of = function
     (* We deal only with the regular cases *)
     | CApp (_,_,l) -> List.fold_left add_var [] (List.map fst l)
-    | CNotation (_,_,(l,[]))
+    | CNotation (_,_,(l,[],[]))
     (* assume the ntn is applicative and does not instantiate the head !! *)
     | CAppExpl (_,_,l) -> List.fold_left add_var [] l
     | CDelimiters(_,_,c) -> vars_of c
@@ -847,7 +1018,7 @@ let rec fold_local_binders g f n acc b = function
       f n (fold_local_binders g f n' acc b l) t
   | LocalRawDef ((_,na),t)::l ->
       f n (fold_local_binders g f (name_fold g na n) acc b l) t
-  | _ ->
+  | [] ->
       f n acc b
 
 let fold_constr_expr_with_binders g f n acc = function
@@ -858,7 +1029,11 @@ let fold_constr_expr_with_binders g f n acc = function
   | CLetIn (_,na,a,b) -> fold_constr_expr_binders g f n acc b [[na],default_binder_kind,a]
   | CCast (loc,a,CastConv(_,b)) -> f n (f n acc a) b
   | CCast (loc,a,CastCoerce) -> f n acc a
-  | CNotation (_,_,(l,ll)) -> List.fold_left (f n) acc (l@List.flatten ll)
+  | CNotation (_,_,(l,ll,bll)) ->
+      (* The following is an approximation: we don't know exactly if
+         an ident is binding nor to which subterms bindings apply *)
+      let acc = List.fold_left (f n) acc (l@List.flatten ll) in
+      List.fold_left (fun acc bl -> fold_local_binders g f n acc (CHole (dummy_loc,None)) bl) acc bll
   | CGeneralization (_,_,_,c) -> f n acc c
   | CDelimiters (loc,_,a) -> f n acc a
   | CHole _ | CEvar _ | CPatVar _ | CSort _ | CPrim _ | CDynamic _  | CRef _ ->
@@ -964,15 +1139,15 @@ let split_at_annot bl na =
   let names = List.map snd (names_of_local_assums bl) in
   match na with
   | None ->
-      if names = [] then error "A fixpoint needs at least one parameter." 
+      if names = [] then error "A fixpoint needs at least one parameter."
       else [], bl
   | Some (loc, id) ->
       let rec aux acc = function
 	| LocalRawAssum (bls, k, t) as x :: rest ->
 	    let l, r = list_split_when (fun (loc, na) -> na = Name id) bls in
-	      if r = [] then aux (x :: acc) rest 
-	      else 
-		(List.rev (if l = [] then acc else LocalRawAssum (l, k, t) :: acc), 
+	      if r = [] then aux (x :: acc) rest
+	      else
+		(List.rev (if l = [] then acc else LocalRawAssum (l, k, t) :: acc),
 		 LocalRawAssum (r, k, t) :: rest)
 	| LocalRawDef _ as x :: rest -> aux (x :: acc) rest
 	| [] ->
@@ -1012,8 +1187,10 @@ let map_constr_expr_with_binders g f e = function
   | CLetIn (loc,na,a,b) -> CLetIn (loc,na,f e a,f (name_fold g (snd na) e) b)
   | CCast (loc,a,CastConv (k,b)) -> CCast (loc,f e a,CastConv(k, f e b))
   | CCast (loc,a,CastCoerce) -> CCast (loc,f e a,CastCoerce)
-  | CNotation (loc,n,(l,ll)) ->
-      CNotation (loc,n,(List.map (f e) l,List.map (List.map (f e)) ll))
+  | CNotation (loc,n,(l,ll,bll)) ->
+      (* This is an approximation because we don't know what binds what *)
+      CNotation (loc,n,(List.map (f e) l,List.map (List.map (f e)) ll,
+                     List.map (fun bl -> snd (map_local_binders f g e bl)) bll))
   | CGeneralization (loc,b,a,c) -> CGeneralization (loc,b,a,f e c)
   | CDelimiters (loc,s,a) -> CDelimiters (loc,s,f e a)
   | CHole _ | CEvar _ | CPatVar _ | CSort _
@@ -1074,16 +1251,21 @@ type 'a module_signature =
   | Check of 'a list (* ... <: T1 <: T2, possibly empty *)
 
 (* Returns the ranges of locs of the notation that are not occupied by args  *)
-(* and which are them occupied by proper symbols of the notation (or spaces) *)
+(* and which are then occupied by proper symbols of the notation (or spaces) *)
 
-let locs_of_notation f loc (args,argslist) ntn =
+let locs_of_notation loc locs ntn =
   let (bl,el) = Util.unloc loc in
+  let locs =  List.map Util.unloc locs in
   let rec aux pos = function
     | [] -> if pos = el then [] else [(pos,el-1)]
-    | a::l ->
-	let ba,ea = Util.unloc (f a) in
-	if pos = ba then aux ea l else (pos,ba-1)::aux ea l
-  in aux bl (args@List.flatten argslist)
+    | (ba,ea)::l ->if pos = ba then aux ea l else (pos,ba-1)::aux ea l
+  in aux bl (Sort.list (fun l1 l2 -> fst l1 < fst l2) locs)
+
+let ntn_loc loc (args,argslist,binderslist) =
+  locs_of_notation loc
+    (List.map constr_loc (args@List.flatten argslist)@
+     List.map local_binders_loc binderslist)
 
-let ntn_loc = locs_of_notation constr_loc
-let patntn_loc = locs_of_notation cases_pattern_expr_loc
+let patntn_loc loc (args,argslist) =
+  locs_of_notation loc
+    (List.map cases_pattern_expr_loc (args@List.flatten argslist))
diff --git a/interp/topconstr.mli b/interp/topconstr.mli
index 5ce488b9a..b5438dd7c 100644
--- a/interp/topconstr.mli
+++ b/interp/topconstr.mli
@@ -31,6 +31,7 @@ type aconstr =
   (** Part only in [rawconstr] *)
   | ALambda of name * aconstr * aconstr
   | AProd of name * aconstr * aconstr
+  | ABinderList of identifier * identifier * aconstr * aconstr
   | ALetIn of name * aconstr * aconstr
   | ACases of case_style * aconstr option *
       (aconstr * (name * (inductive * int * name list) option)) list *
@@ -45,10 +46,33 @@ type aconstr =
   | APatVar of patvar
   | ACast of aconstr * aconstr cast_type
 
+type scope_name = string
+
+type tmp_scope_name = scope_name
+
+type subscopes = tmp_scope_name option * scope_name list
+
+(** Type of the meta-variables of an aconstr: in a recursive pattern x..y,
+    x carries the sequence of objects bound to the list x..y  *)
+type notation_var_instance_type =
+  | NtnTypeConstr | NtnTypeConstrList | NtnTypeBinderList
+
+(** Type of variables when interpreting a constr_expr as an aconstr:
+    in a recursive pattern x..y, both x and y carry the individual type
+    of each element of the list x..y *)
+type notation_var_internalization_type =
+  | NtnInternTypeConstr | NtnInternTypeBinder | NtnInternTypeIdent
+
+(** This characterizes to what a notation is interpreted to *)
+type interpretation =
+    (identifier * (subscopes * notation_var_instance_type)) list * aconstr
+
 (** Translate a rawconstr into a notation given the list of variables
     bound by the notation; also interpret recursive patterns           *)
 
-val aconstr_of_rawconstr : identifier list -> rawconstr -> aconstr
+val aconstr_of_rawconstr :
+  (identifier * notation_var_internalization_type) list ->
+  (identifier * identifier) list -> rawconstr -> aconstr
 
 (** Name of the special identifier used to encode recursive notations  *)
 val ldots_var : identifier
@@ -64,23 +88,14 @@ val rawconstr_of_aconstr_with_binders : loc ->
 
 val rawconstr_of_aconstr : loc -> aconstr -> rawconstr
 
-(** [match_aconstr metas] matches a rawconstr against an aconstr with
-   metavariables in [metas]; raise [No_match] if the matching fails   *)
+(** [match_aconstr] matches a rawconstr against a notation interpretation;
+    raise [No_match] if the matching fails   *)
 
 exception No_match
 
-type scope_name = string
-
-type tmp_scope_name = scope_name
-
-type subscopes = tmp_scope_name option * scope_name list
-
-type interpretation =
-    (** regular vars of notation    / recursive parts of notation    / body *)
-    ((identifier * subscopes) list * (identifier * subscopes) list) * aconstr
-
 val match_aconstr : rawconstr -> interpretation ->
-      (rawconstr * subscopes) list * (rawconstr list * subscopes) list
+      (rawconstr * subscopes) list * (rawconstr list * subscopes) list *
+      (rawdecl list * subscopes) list
 
 val match_aconstr_cases_pattern :  cases_pattern -> interpretation ->
       (cases_pattern * subscopes) list * (cases_pattern list * subscopes) list
@@ -107,19 +122,20 @@ type proj_flag = int option (** [Some n] = proj of the n-th visible argument *)
 
 type prim_token = Numeral of Bigint.bigint | String of string
 
-type 'a notation_substitution =
-    'a list * (** for recursive notations: *) 'a list list
-
 type cases_pattern_expr =
   | CPatAlias of loc * cases_pattern_expr * identifier
   | CPatCstr of loc * reference * cases_pattern_expr list
   | CPatAtom of loc * reference option
   | CPatOr of loc * cases_pattern_expr list
-  | CPatNotation of loc * notation * cases_pattern_expr notation_substitution
+  | CPatNotation of loc * notation * cases_pattern_notation_substitution
   | CPatPrim of loc * prim_token
   | CPatRecord of Util.loc * (reference * cases_pattern_expr) list
   | CPatDelimiters of loc * string * cases_pattern_expr
 
+and cases_pattern_notation_substitution =
+    cases_pattern_expr list *     (** for constr subterms *)
+    cases_pattern_expr list list  (** for recursive notations *)
+
 type constr_expr =
   | CRef of reference
   | CFix of loc * identifier located * fix_expr list
@@ -144,7 +160,7 @@ type constr_expr =
   | CEvar of loc * existential_key * constr_expr list option
   | CSort of loc * rawsort
   | CCast of loc * constr_expr * constr_expr cast_type
-  | CNotation of loc * notation * constr_expr notation_substitution
+  | CNotation of loc * notation * constr_notation_substitution
   | CGeneralization of loc * binding_kind * abstraction_kind option * constr_expr
   | CPrim of loc * prim_token
   | CDelimiters of loc * string * constr_expr
@@ -166,6 +182,11 @@ and local_binder =
   | LocalRawDef of name located * constr_expr
   | LocalRawAssum of name located list * binder_kind * constr_expr
 
+and constr_notation_substitution =
+    constr_expr list *      (** for constr subterms *)
+    constr_expr list list * (** for recursive notations *)
+    local_binder list list (** for binders subexpressions *)
+
 type typeclass_constraint = name located * binding_kind * constr_expr
 
 and typeclass_context = typeclass_constraint list
@@ -178,6 +199,8 @@ val constr_loc : constr_expr -> loc
 
 val cases_pattern_expr_loc : cases_pattern_expr -> loc
 
+val local_binders_loc : local_binder list -> loc
+
 val replace_vars_constr_expr :
   (identifier * identifier) list -> constr_expr -> constr_expr
 
@@ -248,7 +271,6 @@ type 'a module_signature =
   | Check of 'a list (** ... <: T1 <: T2, possibly empty *)
 
 val ntn_loc :
-  Util.loc -> constr_expr notation_substitution -> string -> (int * int) list
+  Util.loc -> constr_notation_substitution -> string -> (int * int) list
 val patntn_loc :
-  Util.loc -> cases_pattern_expr notation_substitution -> string ->
-  (int * int) list
+  Util.loc -> cases_pattern_notation_substitution -> string -> (int * int) list