diff --git a/Partition.mli b/Partition.mli
index 699eac1..03df3ca 100644
--- a/Partition.mli
+++ b/Partition.mli
@@ -43,13 +43,19 @@ module type S =
 
     (** {1 Projection} *)
 
-    (** The value of the call [repr i p] is [Some j], if the item [i]
-        is in the partition [p] and its representative is [j]. If [i]
-        is not in [p], then the value is [None]. *)
-    val repr : item -> partition -> item option
+    (** The value of the call [repr i p] is [j] if the item [i] is in
+        the partition [p] and its representative is [j]. If [i] is not
+        in [p], then the value is [i]. *)
+    val repr : item -> partition -> item
 
-    (** The side-effect of the call [print p] is the printing of the
-        partition [p] on a buffer, based on [Ord.to_string]. *)
+    (** The value of the call [mem i p] is [Some j] if the item [i] is
+        in the partition [p] and its representative is [j]. If [i] is
+        not in [p], then the value is [None]. *)
+    val mem : item -> partition -> item option
+
+    (** The call [print p] is a value of type [Buffer.t] containing
+        strings denoting the partition [p], based on
+        [Ord.to_string]. *)
     val print : partition -> Buffer.t
 
     (** {1 Predicates} *)
@@ -58,7 +64,8 @@ module type S =
         items [i] and [j] belong to the same equivalence class in the
         partition [p], that is, [i] and [j] have the same
         representative. In particular, if either [i] or [j] do not
-        belong to [p], the value of [is_equiv i j p] is [false].*)
+        belong to [p], the value of [is_equiv i j p] is [false]. See
+        [mem] above. *)
     val is_equiv : item -> item -> partition -> bool
   end
 
diff --git a/Partition0.ml b/Partition0.ml
index 6ba824e..cd8b26f 100644
--- a/Partition0.ml
+++ b/Partition0.ml
@@ -2,15 +2,12 @@
 
 module Make (Item: Partition.Item) =
   struct
-
     type item = Item.t
 
     let equal i j = Item.compare i j = 0
 
     module ItemMap = Map.Make (Item)
 
-    type height = int
-
     type partition = item ItemMap.t
     type t = partition
 
@@ -23,14 +20,14 @@ module Make (Item: Partition.Item) =
       else repr parent partition
 
     let is_equiv (i: item) (j: item) (p: partition) : bool =
-      try equal (repr i p) (repr j p) with
-        Not_found -> false
+      try equal (repr i p) (repr j p) with Not_found -> false
 
     let get_or_set (i: item) (p: partition) : item * partition =
       try repr i p, p with Not_found -> i, ItemMap.add i i p
 
-    let repr item partition =
-      try Some (repr item partition) with Not_found -> None
+    let mem i p = try Some (repr i p) with Not_found -> None
+
+    let repr i p = try repr i p with Not_found -> i
 
     let equiv (i: item) (j: item) (p: partition) : partition =
       let ri, p = get_or_set i p in
@@ -48,6 +45,5 @@ module Make (Item: Partition.Item) =
           Printf.sprintf "%s -> %s\n"
                          (Item.to_string src) (Item.to_string dst)
         in Buffer.add_string buffer link
-      in ItemMap.iter print p; buffer
-
+      in (ItemMap.iter print p; buffer)
   end
diff --git a/Partition1.ml b/Partition1.ml
index 07323f4..7d9320a 100644
--- a/Partition1.ml
+++ b/Partition1.ml
@@ -1,5 +1,5 @@
 (* Persistent implementation of Union/Find with height-balanced
-   forests and without path compression: O(n*log(n)).
+   forests and no path compression: O(n*log(n)).
 
    In the definition of type [t], the height component is that of the
    source, that is, if [ItemMap.find i m = (j,h)], then [h] is the
@@ -26,18 +26,18 @@ module Make (Item: Partition.Item) =
       let j, _ as i' = ItemMap.find i p in
       if equal i j then i' else seek j p
 
-    let repr item partition = fst (seek item partition)
+    let repr i p = fst (seek i p)
 
     let is_equiv (i: item) (j: item) (p: partition) : bool =
-      try equal (repr i p) (repr j p) with
-        Not_found -> false
-
-    let repr item partition =
-      try Some (repr item partition) with Not_found -> None
+      try equal (repr i p) (repr j p) with Not_found -> false
 
     let get_or_set (i: item) (p: partition) =
       try seek i p, p with
-        Not_found -> let i' = i,0 in (i', ItemMap.add i i' p)
+        Not_found -> let i' = i,0 in i', ItemMap.add i i' p
+
+    let mem i p = try Some (repr i p) with Not_found -> None
+
+    let repr i p = try repr i p with Not_found -> i
 
     let equiv (i: item) (j: item) (p: partition) : partition =
       let (ri,hi), p = get_or_set i p in
diff --git a/Partition2.ml b/Partition2.ml
index bfb9e26..ef2f7e7 100644
--- a/Partition2.ml
+++ b/Partition2.ml
@@ -1,5 +1,5 @@
 (** Persistent implementation of the Union/Find algorithm with
-    height-balanced forests and without path compression. *)
+    height-balanced forests and no path compression. *)
 
 module Make (Item: Partition.Item) =
   struct
@@ -59,19 +59,20 @@ module Make (Item: Partition.Item) =
            Root hi -> i,hi
       | Link (j,_) -> seek j p
 
-    let repr item partition = fst (seek item partition)
+    let repr i p = fst (seek i p)
 
     let is_equiv (i: item) (j: item) (p: partition) : bool =
       try equal (repr i p) (repr j p) with
         Not_found -> false
 
-    let repr item partition =
-      try Some (repr item partition) with Not_found -> None
-
     let get_or_set (i: item) (p: partition) =
       try seek i p, p with
         Not_found -> let n = i,0 in (n, root n p)
 
+    let mem i p = try Some (repr i p) with Not_found -> None
+
+    let repr i p = try repr i p with Not_found -> i
+
     let equiv (i: item) (j: item) (p: partition) : partition =
       let (ri,hi as ni), p = get_or_set i p in
       let (rj,hj as nj), p = get_or_set j p in
diff --git a/Partition3.ml b/Partition3.ml
index e831990..42fcd7a 100644
--- a/Partition3.ml
+++ b/Partition3.ml
@@ -14,7 +14,11 @@ module Make (Item: Partition.Item) =
         upwardly and otherwise is a link to another node. Those trees
         are height-balanced. The type [node] implements nodes in those
         trees. *)
-    type node = {item: item; mutable height: int; mutable parent: node}
+    type node = {
+                item : item;
+      mutable height : int;
+      mutable parent : node
+    }
 
     module ItemMap = Map.Make (Item)
 
@@ -39,21 +43,22 @@ module Make (Item: Partition.Item) =
         if node.parent == node then node else find_root node.parent
       in find_root (ItemMap.find i p)
 
-    let repr item partition = (seek item partition).item
+    let repr i p = (seek i p).item
 
     let is_equiv (i: item) (j: item) (p: partition) : bool =
       try equal (repr i p) (repr j p) with
         Not_found -> false
 
-    let repr item partition =
-      try Some (repr item partition) with Not_found -> None
-
     let get_or_set item (p: partition) =
       try seek item p, p with
         Not_found ->
           let rec loop = {item; height=0; parent=loop}
           in loop, ItemMap.add item loop p
 
+    let mem i p = try Some (repr i p) with Not_found -> None
+
+    let repr i p = try repr i p with Not_found -> i
+
     let link src dst = src.parent <- dst
 
     let equiv (i: item) (j: item) (p: partition) : partition =