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diff --git a/src/tree/splay.ml b/src/tree/splay.ml
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+module type KEY = sig
+
+ type 'a t
+
+ (** Parametrized comparator *)
+ val comp: 'a t -> 'b t -> ('a, 'b) Tools.cmp
+
+ val repr: Format.formatter -> 'a t -> unit
+
+end
+
+module Make (El : KEY) = struct
+
+ type container = C : ('a El.t * 'a) -> container [@@unboxed]
+
+ type leaf (** Fantom type for typing the tree *)
+ type node (** Fantom type for typing the tree *)
+
+ type 'a branch =
+ | Leaf : leaf branch
+ | Node : _ branch * ('a El.t * 'a) * _ branch -> node branch
+
+ type t = T : 'a branch ref -> t [@@unboxed]
+
+ let empty = T (ref Leaf)
+
+ let isEmpty (T tree) = match !tree with
+ | Leaf -> true
+ | _ -> false
+
+ let rec splay : type a. a El.t -> node branch -> node branch = fun x t -> begin
+ let Node (l, y, r) = t in
+ begin match El.comp x (fst y) with
+ | Tools.Eq -> t
+ | Tools.Lt ->
+ begin match l with
+ | Leaf -> t
+ | Node (ll, z, rr) ->
+ begin match El.comp x (fst z) with
+ | Tools.Eq -> Node (ll, z, Node (rr, y, r))
+ | Tools.Lt ->
+ begin match ll with
+ | Leaf -> Node (ll, z, Node (rr, y, r))
+ | Node _ as ll ->
+ let Node (newL, newV, newR) = splay x ll
+ in Node (newL, newV, Node (newR, z, Node (rr, y, r)))
+ end
+ | Tools.Gt ->
+ begin match rr with
+ | Leaf -> Node (ll, z, Node (rr, y, r))
+ | Node _ as rr ->
+ let Node (newL, newV, newR) = splay x rr
+ in Node (Node (ll, z, newL), newV, Node (newR, y, r))
+ end
+ end
+ end
+ | Tools.Gt ->
+ begin match r with
+ | Leaf -> t
+ | Node (ll, z, rr) ->
+ begin match El.comp x (fst z) with
+ | Tools.Eq -> Node (Node (l, y, ll), z, rr)
+ | Tools.Lt ->
+ begin match ll with
+ | Leaf -> Node (Node (l, y, ll), z, rr)
+ | Node _ as ll ->
+ let Node (newL, newV, newR) = splay x ll
+ in Node (Node (l, y, newL), newV, Node (newR, z, rr))
+ end
+ | Tools.Gt ->
+ begin match rr with
+ | Leaf -> Node (Node (l, y, ll), z, rr)
+ | Node _ as rr ->
+ let Node (newL, newV, newR) = splay x rr
+ in Node (Node (Node(l, y, ll), z, newL), newV, newR)
+ end
+ end
+ end
+ end
+ end
+
+ let member: type a. a El.t -> t -> bool = fun x (T t) -> match !t with
+ | Leaf -> false
+ | Node _ as root ->
+ let root' = splay x root in
+ t := root';
+ let Node (_, c', _) = root' in
+ begin match El.comp (fst c') x with
+ | Tools.Eq -> true
+ | _ -> false
+ end
+
+ let find: type a. a El.t -> t -> a = fun x (T t) -> match !t with
+ | Leaf -> raise Not_found
+ | Node _ as root ->
+ let root' = splay x root in
+ t := root';
+ let Node (_, c', _) = root' in
+ begin match El.comp (fst c') x with
+ | Tools.Eq -> snd c'
+ | _ -> raise Not_found
+ end
+
+ let add: type a. a El.t -> a -> t -> t = fun key value (T t) -> match !t with
+ | Leaf -> T (ref (Node (Leaf, (key, value), Leaf)))
+ | Node _ as root ->
+ let root' = splay key root in
+ let Node (l, y, r) = root' in
+ begin match El.comp key (fst y) with
+ | Tools.Eq -> T (ref (Node(l, (key, value), r)))
+ | Tools.Lt -> T (ref (Node (l, (key, value), Node (Leaf, y, r))))
+ | Tools.Gt -> T (ref (Node (Node (l, y, Leaf), (key, value), r)))
+ end
+
+ let rec _subtree_maximum:type a. a branch -> a branch = fun t -> begin match t with
+ | Leaf -> Leaf
+ | Node (_, _, (Node (_, _, _) as x)) -> _subtree_maximum x
+ | Node (_, (key, value), Leaf) -> splay key t
+ end
+
+ let rec _subtree_minimum: type a. a branch -> a branch = fun t -> begin match t with
+ | Leaf -> Leaf
+ | Node ((Node (_, _, _) as x), _, _) -> _subtree_minimum x
+ | Node (Leaf, (key, value), _) -> splay key t
+ end
+
+ let remove: type a. a El.t -> t -> t = fun key (T t) -> begin match !t with
+ | Leaf -> empty
+ | Node _ as root ->
+ let root' = splay key root in
+ let Node (l, c', r) = root' in
+ begin match El.comp (fst c') key with
+ | Tools.Eq -> begin match _subtree_maximum l with
+ | Node(l, c, Leaf) -> T (ref (Node(l, c, r)))
+ | Node(l, c, _) -> raise Not_found
+ | Leaf -> begin match _subtree_minimum r with
+ | Leaf -> empty
+ | Node(Leaf, c, r) -> T (ref (Node(l, c, r)))
+ | Node(_, c, r) -> raise Not_found
+ end
+ end
+ (* The key is not present, return the splayed tree *)
+ | _ -> T (ref root')
+ end
+ end
+
+ (** Existencial type for the branches *)
+ type exBranch = Branch : _ branch -> exBranch [@@unboxed]
+
+ let fold f init (T t) = begin
+ let rec _fold : type b. (container * exBranch) list -> 'a -> b branch -> 'a = begin
+ fun acc v -> function
+ (* We have a node : we accumulate the right part, and process the left branch *)
+ | Node (left, (key, value), right) ->
+ let c = C (key, value) in
+ (_fold [@tailcall]) ((c, Branch right)::acc) v left
+ (* We have nothing left, we process the values delayed *)
+ | Leaf -> begin match acc with
+ | [] -> v
+ | (c, (Branch right))::tl -> (_fold [@tailcall]) tl (f v c) right
+ end
+ end in
+ _fold [] init !t
+ end
+
+ let repr formatter (T t) = begin
+
+ let repr_edge from formatter dest = begin
+ Format.fprintf formatter "\"%a\" -> \"%a\"\n"
+ El.repr from
+ El.repr dest
+ end in
+
+ let rec repr': type a b. a El.t -> Format.formatter -> b branch -> unit = fun parent formatter -> function
+ | Leaf -> ()
+ | Node (l, c, r) ->
+ let key = fst c in
+ Format.fprintf formatter "%a%a%a"
+ (repr_edge parent) key
+ (repr' key) l
+ (repr' key) r in
+
+ begin match !t with
+ | Leaf -> Format.fprintf formatter "digraph G {}"
+ | Node (l, c, r) ->
+ let key = fst c in
+ Format.fprintf formatter "digraph G {\n%a%a}"
+ (repr' key) l
+ (repr' key) r
+ end
+
+ end
+
+end
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