diff --git a/splayTree.ml b/splayTree.ml
index 6777ed85..f520e56a 100644
--- a/splayTree.ml
+++ b/splayTree.ml
@@ -43,23 +43,98 @@ let is_empty (tree, _) =
   | Empty -> true
   | Node _ -> false
 
-let rec bigger ~cmp pivot tree =
+(** Partition the tree into (elements <= pivot, elements > pivot) *)
+let rec partition ~cmp pivot tree =
   match tree with
-  | Empty -> Empty
+  | Empty -> Empty, Empty
   | Node (a, x, x_val, b) ->
     if cmp x pivot <= 0
-      then bigger ~cmp pivot b
-      else match a with
-        | Empty -> Node (Empty, x, x_val, b)
+      then begin
+        match b with
+        | Empty -> (tree, Empty)
+        | Node (b1, y, y_val, b2) ->
+          if cmp y pivot <= 0
+            then
+              let small, big = partition ~cmp pivot b2 in
+              Node (Node (a, x, x_val, b1), y, y_val, small), big
+            else
+              let small, big = partition ~cmp pivot b1 in
+              Node (a, x, x_val, small), Node (big, y, y_val, b2)
+      end else begin
+        match a with
+        | Empty -> (Empty, tree)
         | Node (a1, y, y_val, a2) ->
           if cmp y pivot <= 0
-            then Node (bigger ~cmp pivot a2, x, x_val, b)
-            else Node (bigger ~cmp pivot a1, y, y_val, Node (a2, x, x_val, b))
-
-let rec smaller ~cmp pivot tree =
+            then
+              let small, big = partition ~cmp pivot a2 in
+              Node (a1, y, y_val, small), Node (big, x, x_val, b)
+            else
+              let small, big = partition ~cmp pivot a1 in
+              small, Node (big, y, y_val, Node (a2, x, x_val, b))
+      end
 
 (** Insert the pair (key -> value) in the tree *)
 let insert (tree, cmp) k v =
-  let tree' = Node (smaller ~cmp k tree, k, v, bigger ~cmp k tree) in
+  let small, big = partition ~cmp k tree in
+  let tree' = Node (small, k, v, big) in
   tree', cmp
 
+let remove (tree, cmp) k = failwith "not implemented"
+
+let replace (tree, cmp) k = failwith "not implemented"
+
+(** Returns the top value, or raise Not_found is empty *)
+let top (tree, _) =
+  match tree with
+  | Empty -> raise Not_found
+  | Node (_, k, v, _) -> k, v
+
+(** Access minimum value *)
+let min (tree, _) =
+  let rec min tree =
+    match tree with
+    | Empty -> raise Not_found
+    | Node (Empty, k, v, _) -> k, v
+    | Node (l, _, _, _) -> min l
+  in min tree
+
+(** Get minimum value and remove it from the tree *)
+let delete_min (tree, cmp) =
+  let rec delete_min tree = match tree with
+  | Empty -> raise Not_found
+  | Node (Empty, x, x_val, b) -> x, x_val, b
+  | Node (Node (Empty, x, x_val, b), y, y_val, c) ->
+    x, x_val, Node (b, y, y_val, c)  (* rebalance *)
+  | Node (Node (a, x, x_val, b), y, y_val, c) ->
+    let m, m_val, a' = delete_min a in
+    m, m_val, Node (a', x, x_val, Node (b, y, y_val, c))
+  in
+  let m, m_val, tree' = delete_min tree in
+  m, m_val, (tree', cmp)
+
+(** Find the value for the given key (or raise Not_found).
+    It also returns the splayed tree *)
+let find (tree, cmp) k =
+  failwith "not implemented" 
+
+let find_fold (tree, cmp) k f acc =
+  acc (* TODO *)
+
+(** Iterate on elements *)
+let iter (tree, _) f =
+  let rec iter tree =
+    match tree with
+    | Empty -> ()
+    | Node (a, x, x_val, b) ->
+      iter a;
+      f x x_val;
+      iter b
+  in iter tree
+
+(** Number of elements (linear) *)
+let size t =
+  let r = ref 0 in
+  iter t (fun _ _ -> incr r);
+  !r
+
+let get_cmp (_, cmp) = cmp
diff --git a/splayTree.mli b/splayTree.mli
index 08adcc44..dab3b18e 100644
--- a/splayTree.mli
+++ b/splayTree.mli
@@ -31,7 +31,7 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 type ('a, 'b) t
   (** A functional splay tree *)
 
-val empty : cmp:('a -> 'a -> bool) -> ('a, 'b) t
+val empty : cmp:('a -> 'a -> int) -> ('a, 'b) t
   (** Empty splay tree using the given comparison function *)
 
 val is_empty : (_, _) t -> bool
@@ -40,26 +40,34 @@ val is_empty : (_, _) t -> bool
 val insert : ('a, 'b) t -> 'a -> 'b -> ('a, 'b) t
   (** Insert the pair (key -> value) in the tree *)
 
+val remove : ('a, 'b) t -> 'a -> ('a, 'b) t
+  (** Remove an element by its key, returns the splayed tree *)
+
 val replace : ('a, 'b) t -> 'a -> 'b -> ('a, 'b) t
   (** Insert the pair (key -> value) into the tree, replacing
       the previous binding (if any). It replaces at most one
       binding. *)
 
-val remove : ('a, 'b) t -> 'a -> ('a, 'b) t
-  (** Remove an element by its key, returns the splayed tree *)
-
-val top : ('a, b') t -> 'a * 'b
+val top : ('a, 'b) t -> 'a * 'b
   (** Returns the top value, or raise Not_found is empty *)
 
-val min : ('a, 'b) t -> 'a * 'b * ('a, b') t
+val min : ('a, 'b) t -> 'a * 'b
   (** Access minimum value *)
 
+val delete_min : ('a, 'b) t -> 'a * 'b * ('a, 'b) t
+  (** Get minimum value and remove it from the tree *)
+
 val find : ('a, 'b) t -> 'a -> 'b * ('a, 'b) t
   (** Find the value for the given key (or raise Not_found).
       It also returns the splayed tree *)
 
+val find_fold : ('a, 'b) t -> 'a -> ('c -> 'b -> 'c) -> 'c -> 'c
+  (** Fold on all values associated with the given key *)
+
+val iter : ('a, 'b) t -> ('a -> 'b -> unit) -> unit
+  (** Iterate on elements *)
+
 val size : (_, _) t -> int
   (** Number of elements (linear) *)
 
-val iter : ('a -> 'b -> unit) -> ('a, 'b) t -> unit
-  (** Iterate on elements *)
+val get_cmp : ('a, _) t -> ('a -> 'a -> int)