diff --git a/src/ciclib/bvar.ml b/src/ciclib/bvar.ml
index 279a33fb..7cff282a 100644
--- a/src/ciclib/bvar.ml
+++ b/src/ciclib/bvar.ml
@@ -1,6 +1,6 @@
 open Types_
 
-type t = bvar = { bv_idx: int }
+type t = bvar = { bv_idx: int } [@@unboxed]
 
 let equal (v1 : t) v2 = v1.bv_idx = v2.bv_idx
 let hash v = H.combine2 10 (H.int v.bv_idx)
diff --git a/src/ciclib/bvar.mli b/src/ciclib/bvar.mli
index 22324af4..8bb5f37e 100644
--- a/src/ciclib/bvar.mli
+++ b/src/ciclib/bvar.mli
@@ -2,7 +2,7 @@
 
 open Types_
 
-type t = bvar = { bv_idx: int }
+type t = bvar = { bv_idx: int } [@@unboxed]
 
 include EQ_HASH_PRINT with type t := t
 
diff --git a/src/ciclib/const.ml b/src/ciclib/const.ml
index be11effc..2cd25624 100644
--- a/src/ciclib/const.ml
+++ b/src/ciclib/const.ml
@@ -1,8 +1,7 @@
 open Types_
 
-type t = const = { c_name: string; c_ty: term }
+type t = const = { c_name: string } [@@unboxed]
 
 let[@inline] name self = self.c_name
-let[@inline] ty self = self.c_ty
 let pp out (a : t) = Fmt.string out a.c_name
-let make c_name ~ty:c_ty : t = { c_name; c_ty }
+let make c_name : t = { c_name }
diff --git a/src/ciclib/const.mli b/src/ciclib/const.mli
index 9e63fd8f..5c81332d 100644
--- a/src/ciclib/const.mli
+++ b/src/ciclib/const.mli
@@ -7,7 +7,6 @@ open Types_
 type t = const
 
 val name : t -> string
-val make : string -> ty:term -> t
-val ty : t -> term
+val make : string -> t
 
 include PRINT with type t := t
diff --git a/src/ciclib/level.ml b/src/ciclib/level.ml
index 9e178d14..e0e42a6d 100644
--- a/src/ciclib/level.ml
+++ b/src/ciclib/level.ml
@@ -45,7 +45,7 @@ let rec is_ground (l : t) : bool =
 
 let zero : t = L_zero
 let[@inline] succ t : t = L_succ t
-let[@inline] one = succ zero
+let one = succ zero
 let[@inline] var n : t = L_var n
 
 let rec max a b : t =
diff --git a/src/ciclib/term.ml b/src/ciclib/term.ml
index c2778d82..6508179e 100644
--- a/src/ciclib/term.ml
+++ b/src/ciclib/term.ml
@@ -2,14 +2,15 @@ open Types_
 
 type bvar = Bvar.t
 type nonrec term = term
+type nonrec binder = binder = BD | BI | BS | BC
 
 type view = term_view =
   | E_type of level
   | E_bound_var of bvar
-  | E_const of const
+  | E_const of const * level list
   | E_app of term * term
-  | E_lam of term * term
-  | E_pi of term * term
+  | E_lam of binder * string * term * term
+  | E_pi of binder * string * term * term
 
 type t = term
 
@@ -47,6 +48,12 @@ let as_type e : level option =
   | E_type l -> Some l
   | _ -> None
 
+let string_of_binder = function
+  | BI -> "BI"
+  | BS -> "BS"
+  | BC -> "BC"
+  | BD -> "BD"
+
 (* debug printer *)
 let expr_pp_with_ ~max_depth out (e : term) : unit =
   let rec loop k ~depth names out e =
@@ -59,17 +66,21 @@ let expr_pp_with_ ~max_depth out (e : term) : unit =
       (match CCList.nth_opt names idx with
       | Some n when n <> "" -> Fmt.fprintf out "%s[%d]" n idx
       | _ -> Fmt.fprintf out "_[%d]" idx)
-    | E_const c -> Const.pp out c
+    | E_const (c, []) -> Const.pp out c
+    | E_const (c, args) ->
+      Fmt.fprintf out "(@[%a@ %a@])" Const.pp c (Util.pp_list Level.pp) args
     | (E_app _ | E_lam _) when depth > max_depth -> Fmt.fprintf out "@<1>…"
     | E_app _ ->
       let f, args = unfold_app e in
       Fmt.fprintf out "(%a@ %a)" pp' f (Util.pp_list pp') args
-    | E_lam (_ty, bod) ->
-      Fmt.fprintf out "(@[\\_:@[%a@].@ %a@])" pp' _ty
+    | E_lam (binder, name, _ty, bod) ->
+      Fmt.fprintf out "(@[\\[%s]%s:@[%a@].@ %a@])" (string_of_binder binder)
+        name pp' _ty
         (loop (k + 1) ~depth:(depth + 1) ("" :: names))
         bod
-    | E_pi (ty_arg, bod) ->
-      Fmt.fprintf out "(@[Pi _:@[%a@].@ %a@])" pp' ty_arg
+    | E_pi (binder, name, ty_arg, bod) ->
+      Fmt.fprintf out "(@[Pi[%s] %s:@[%a@].@ %a@])" (string_of_binder binder)
+        name pp' ty_arg
         (loop (k + 1) ~depth:(depth + 1) ("" :: names))
         bod
   in
@@ -93,7 +104,7 @@ let iter_shallow ~f (e : term) : unit =
     | E_app (hd, a) ->
       f false hd;
       f false a
-    | E_lam (tyv, bod) | E_pi (tyv, bod) ->
+    | E_lam (_, _, tyv, bod) | E_pi (_, _, tyv, bod) ->
       f false tyv;
       f true bod)
 
@@ -125,7 +136,7 @@ let compute_db_depth_ e : int =
       | E_type _ | E_const _ -> 0
       | E_bound_var v -> v.bv_idx + 1
       | E_app (a, b) -> max (db_depth a) (db_depth b)
-      | E_lam (ty, bod) | E_pi (ty, bod) ->
+      | E_lam (_, _, ty, bod) | E_pi (_, _, ty, bod) ->
         max (db_depth ty) (max 0 (db_depth bod - 1))
     in
     d
@@ -147,20 +158,20 @@ let map_shallow ~f (e : term) : term =
       e
     else
       make_ (E_app (f false hd, f false a))
-  | E_lam (tyv, bod) ->
+  | E_lam (b, name, tyv, bod) ->
     let tyv' = f false tyv in
     let bod' = f true bod in
     if tyv == tyv' && bod == bod' then
       e
     else
-      make_ (E_lam (tyv', bod'))
-  | E_pi (tyv, bod) ->
+      make_ (E_lam (b, name, tyv', bod'))
+  | E_pi (b, name, tyv, bod) ->
     let tyv' = f false tyv in
     let bod' = f true bod in
     if tyv == tyv' && bod == bod' then
       e
     else
-      make_ (E_pi (tyv', bod'))
+      make_ (E_pi (b, name, tyv', bod'))
 
 (* shift open bound variables of [e] by [n] *)
 let db_shift_ ~make (e : term) (n : int) =
@@ -226,11 +237,11 @@ let type_of_univ_int i : term = type_of_univ (Level.of_int i)
 let type_ : term = type_of_univ Level.one
 let bvar v : term = make_ (E_bound_var v)
 let bvar_i i : term = make_ (E_bound_var (Bvar.make i))
-let const c : term = make_ (E_const c)
+let const c args : term = make_ (E_const (c, args))
 let app f a = make_ (E_app (f, a))
 let app_l f l = List.fold_left app f l
-let lam ~var_ty bod : term = make_ (E_lam (var_ty, bod))
-let pi ~var_ty bod : term = make_ (E_pi (var_ty, bod))
+let lam b str ~var_ty bod : term = make_ (E_lam (b, str, var_ty, bod))
+let pi b str ~var_ty bod : term = make_ (E_pi (b, str, var_ty, bod))
 
 module DB = struct
   let subst_db0 e ~by : t = db_0_replace_ ~make:make_ e ~by
diff --git a/src/ciclib/term.mli b/src/ciclib/term.mli
index be73c036..7565c597 100644
--- a/src/ciclib/term.mli
+++ b/src/ciclib/term.mli
@@ -15,16 +15,18 @@ type nonrec term = term
 type t = term
 (** A term, in the calculus of constructions *)
 
+type nonrec binder = binder = BD | BI | BS | BC
+
 (** View.
 
     A view is the shape of the root node of a term. *)
 type view = term_view =
   | E_type of level
   | E_bound_var of bvar
-  | E_const of const
+  | E_const of const * level list
   | E_app of t * t
-  | E_lam of t * t
-  | E_pi of t * t
+  | E_lam of binder * string * t * t
+  | E_pi of binder * string * t * t
 
 val pp_debug : t Fmt.printer
 
@@ -61,11 +63,11 @@ val type_of_univ : level -> t
 val type_of_univ_int : int -> t
 val bvar : bvar -> t
 val bvar_i : int -> t
-val const : const -> t
+val const : const -> level list -> t
 val app : t -> t -> t
 val app_l : t -> t list -> t
-val lam : var_ty:t -> t -> t
-val pi : var_ty:t -> t -> t
+val lam : binder -> string -> var_ty:t -> t -> t
+val pi : binder -> string -> var_ty:t -> t -> t
 
 (** De bruijn indices *)
 module DB : sig
diff --git a/src/ciclib/types_.ml b/src/ciclib/types_.ml
index e42983e0..c62e1670 100644
--- a/src/ciclib/types_.ml
+++ b/src/ciclib/types_.ml
@@ -1,5 +1,7 @@
 module H = CCHash
 
+type binder = BD | BI | BS | BC
+
 (** A level expression *)
 type level =
   | L_zero
@@ -11,13 +13,13 @@ type level =
 type term_view =
   | E_type of level
   | E_bound_var of bvar
-  | E_const of const
+  | E_const of const * level list  (** constant instantiated with universes *)
   | E_app of term * term
-  | E_lam of term * term
-  | E_pi of term * term
+  | E_lam of binder * string * term * term
+  | E_pi of binder * string * term * term
 
-and bvar = { bv_idx: int }
-and const = { c_name: string; c_ty: term }
+and bvar = { bv_idx: int } [@@unboxed]
+and const = { c_name: string } [@@unboxed]
 
 and term = {
   view: term_view;