diff --git a/src/lfu.mli b/src/lfu.mli
index 8f2daf7..f8d20a6 100644
--- a/src/lfu.mli
+++ b/src/lfu.mli
@@ -2,20 +2,74 @@ module Make (K : sig
   type t
 
   val equal : t -> t -> bool
+  (*@ pure*)
+
   val hash : t -> int
 end) : sig
-  type 'a t
   type key = K.t
 
+  type 'a t
+  
+  (*@ ephemeral
+      model cap : int
+      mutable model assoc : key -> 'a option
+      mutable model frequency : key -> int
+      invariant cap > 0
+      invariant forall k. assoc k <> None <-> frequency k > 0 *)
+
   val v : int -> 'a t
+  (* t = v c
+     checks c > 0
+     ensures t.cap = c
+     ensures forall k. t.assoc k = None *)
+
   val stats : 'a t -> Stats.t
   val is_empty : 'a t -> bool
+  (*@ b = is_empty t
+      pure
+      ensures b <-> forall k. t.assoc k = None *)
+
   val capacity : 'a t -> int
+  (*@ c = capacity t
+      pure
+      ensures c = t.cap *)
+
   val size : 'a t -> int
+  (*@ s = size t
+      pure 
+      ensures s <= t.cap *)
+
   val clear : 'a t -> unit
+  (*@ clear t
+      modifies t 
+      ensures forall k. t.assoc k = None *)
+
   val find : 'a t -> key -> 'a
+  (*@ v = find t k
+      ensures t.assoc k = Some v -> t.frequency k = t.frequency (old k) + 1
+      raises Not_found -> t.assoc k = None *)
+
   val find_opt : 'a t -> key -> 'a option
+  (*@ o = find_opt t k
+      pure
+      ensures o = t.assoc k
+      ensures t.assoc k <> None -> t.frequency k = t.frequency (old k) + 1 *)
+
   val mem : 'a t -> key -> bool
+  (*@ b = mem t k
+      pure
+      ensures b <-> t.assoc k <> None && t.frequency k = t.frequency (old k) + 1 *)
+
   val replace : 'a t -> key -> 'a -> unit
+  (*@ replace t k v
+      modifies t
+      ensures t.assoc k = Some v
+      ensures t.assoc (old k) <> None -> t.frequency k = t.frequency (old k) + 1
+      ensures t.assoc (old k) = None ->
+        forall k', v'. t.assoc (old k') = Some v' -> t.assoc k' = Some v' && t.frequency k = 1 *)
+
   val remove : 'a t -> key -> unit
+  (*@ remove t k
+      modifies t
+      ensures t.assoc k = None *)
 end
diff --git a/src/lru.mli b/src/lru.mli
index a295c39..4badaec 100644
--- a/src/lru.mli
+++ b/src/lru.mli
@@ -47,10 +47,10 @@ end) : sig
       raises Not_found -> t.assoc k = None *)
 
   val find_opt : 'a t -> key -> 'a option
-
   (*@ o = find_opt t k
       ensures o = t.assoc k *)
-  val mem : 'a t -> key -> bool
+ 
+      val mem : 'a t -> key -> bool
   (*@ b = mem t k
       ensures b = true <-> t.assoc k <> None *)
 
diff --git a/src/stats.ml b/src/stats.ml
index fd80969..4a94d11 100644
--- a/src/stats.ml
+++ b/src/stats.ml
@@ -32,7 +32,7 @@ let add new_size t =
   t.add <- t.add + 1;
   if t.max_size < new_size then t.max_size <- new_size
 
-let pp ppf t =
+(* let pp ppf t =
   Fmt.pf ppf
     {|miss             : %d
   hit              : %d
@@ -42,4 +42,4 @@ let pp ppf t =
   remove           : %d
   clear            : %d
   maximal size     : %d|}
-    t.miss t.hit t.add t.replace t.discard t.remove t.clear t.max_size
+    t.miss t.hit t.add t.replace t.discard t.remove t.clear t.max_size *)
diff --git a/src/stats.mli b/src/stats.mli
index d3ac3ad..8251a05 100644
--- a/src/stats.mli
+++ b/src/stats.mli
@@ -64,4 +64,5 @@ val add : int -> t -> unit
   ensures  t.max_size >= old t.max_size
 *)
 
-val pp : Format.formatter -> t -> unit
+(* val pp : Format.formatter -> t -> unit *)
+