diff --git a/src/flow/binary.rs b/src/flow/binary.rs
index 1bf95d4..c95b5e5 100644
--- a/src/flow/binary.rs
+++ b/src/flow/binary.rs
@@ -2,6 +2,8 @@ use std::rc::Rc;
 
 use crate::func::*;
 
+use super::comparator::Comparator;
+
 pub type NodeRc<'a, BT> = Rc<<BT as BinaryTrees<'a>>::Node>;
 pub type ReferenceRc<'a, BT> = Rc<<BT as BinaryTrees<'a>>::Reference>;
 pub type TreeRc<'a, BT> = Rc<<BT as BinaryTrees<'a>>::Tree>;
@@ -17,22 +19,29 @@ pub trait BinaryTrees<'a>: 'a {
     type Reference: 'a;
     type Tree: 'a;
     type Key: 'a;
+    type Comparator: Comparator<Self::Key>;
 
     type T: Monad<'a>;
 
-    fn split(node: Self::Node) -> Split<'a, Self>;
-    fn to_tree(node: Self::Node) -> TreeRc<'a, Self>;
-    fn resolve(reference: Self::Reference) -> Wrapped<'a, Self, NodeRc<'a, Self>>;
-    fn equal(rhs: Self::Reference, lhs: Self::Reference) -> bool;
-    fn refer(tree: Self::Tree) -> Option<ReferenceRc<'a, Self>>;
+    fn comparator(&self) -> &Self::Comparator;
+    fn split(&self, node: Self::Node) -> Split<'a, Self>;
+    fn to_tree(&self, node: Self::Node) -> TreeRc<'a, Self>;
+    fn resolve(&self, reference: Self::Reference) -> Wrapped<'a, Self, NodeRc<'a, Self>>;
+    fn equal(&self, rhs: Self::Reference, lhs: Self::Reference) -> bool;
+    fn refer(&self, tree: Self::Tree) -> Option<ReferenceRc<'a, Self>>;
 }
 
 pub trait BinaryTreesMutable<'a>: BinaryTrees<'a> {
     fn join_key(
+        &self,
         tl: Self::Tree,
         key: KeyRc<'a, Self>,
         tr: Self::Tree,
-    ) -> Wrapped<'a, Self, TreeRc<'a, Self>>;
-    fn join(tl: Self::Tree, tr: Self::Tree) -> Wrapped<'a, Self, TreeRc<'a, Self>>;
-    fn split_key(tree: Self::Tree, key: KeyRc<'a, Self>) -> Wrapped<'a, Self, KeySplit<'a, Self>>;
+    ) -> Wrapped<'a, Self, NodeRc<'a, Self>>;
+    fn join(&self, tl: Self::Tree, tr: Self::Tree) -> Wrapped<'a, Self, TreeRc<'a, Self>>;
+    fn split_key(
+        &self,
+        tree: Self::Tree,
+        key: KeyRc<'a, Self>,
+    ) -> Wrapped<'a, Self, KeySplit<'a, Self>>;
 }