diff --git a/crates/loro-core/Cargo.toml b/crates/loro-core/Cargo.toml
index 1544cbf0..c2cc1374 100644
--- a/crates/loro-core/Cargo.toml
+++ b/crates/loro-core/Cargo.toml
@@ -16,7 +16,13 @@ moveit = "0.5.0"
 pin-project = "1.0.10"
 serde = {version = "1.0.140", features = ["derive"]}
 thiserror = "1.0.31"
+im = "15.1.0"
 
 [dev-dependencies]
 proptest = "1.0.0"
 proptest-derive = "0.3.0"
+rand = "0.8.5"
+
+# See https://matklad.github.io/2021/02/27/delete-cargo-integration-tests.html
+[lib]
+doctest = false
diff --git a/crates/loro-core/justfile b/crates/loro-core/justfile
new file mode 100644
index 00000000..164a1fb4
--- /dev/null
+++ b/crates/loro-core/justfile
@@ -0,0 +1,18 @@
+build:
+  cargo build
+
+test:
+  cargo nextest run
+
+# test without proptest
+test-fast:
+  RUSTFLAGS='--cfg no_proptest' cargo nextest run
+
+check-unsafe:
+  env RUSTFLAGS="-Funsafe-code --cap-lints=warn" cargo check
+
+deny:
+  cargo deny check
+
+crev:
+  cargo crev crate check
diff --git a/crates/loro-core/src/change.rs b/crates/loro-core/src/change.rs
index 6d458363..771b3749 100644
--- a/crates/loro-core/src/change.rs
+++ b/crates/loro-core/src/change.rs
@@ -1,3 +1,9 @@
+//! [Change]s are merged ops.
+//!
+//! Every [Change] has deps on other [Change]s. All [Change]s in the document thus form a DAG.
+//! Note, `dep` may point to the middle of the other [Change].
+//!
+//! In future, we may also use [Change] to represent a transaction. But this decision is postponed.
 use std::char::MAX;
 
 use crate::{
@@ -97,7 +103,7 @@ impl Mergable<ChangeMergeCfg> for Change {
         }
 
         if other.deps.is_empty()
-            || (other.deps.len() == 1 && self.id.is_connected_id(&other.deps[0], self.len() as u32))
+            || (other.deps.len() == 1 && self.id.is_connected_id(&other.deps[0], self.len()))
         {
             return false;
         }
@@ -111,7 +117,7 @@ impl Mergable<ChangeMergeCfg> for Change {
         }
 
         self.id.client_id == other.id.client_id
-            && self.id.counter + self.len() as u32 == other.id.counter
+            && self.id.counter + self.len() as Counter == other.id.counter
             && self.lamport + self.len() as Lamport == other.lamport
     }
 }
diff --git a/crates/loro-core/src/container/map/map_container.rs b/crates/loro-core/src/container/map/map_container.rs
index 08159f58..3baa62bb 100644
--- a/crates/loro-core/src/container/map/map_container.rs
+++ b/crates/loro-core/src/container/map/map_container.rs
@@ -70,6 +70,15 @@ impl MapContainer {
             },
         }]);
 
+        if self.value.is_some() {
+            self.value
+                .as_mut()
+                .unwrap()
+                .as_map_mut()
+                .unwrap()
+                .insert(key.clone(), value.clone().into());
+        }
+
         self.state.insert(
             key,
             ValueSlot {
@@ -120,6 +129,15 @@ impl Container for MapContainer {
                             counter: op.id().counter,
                         },
                     );
+
+                    if self.value.is_some() {
+                        self.value
+                            .as_mut()
+                            .unwrap()
+                            .as_map_mut()
+                            .unwrap()
+                            .insert(v.key.clone(), v.value.clone().into());
+                    }
                 }
             }
             _ => unreachable!(),
diff --git a/crates/loro-core/src/container/map/tests.rs b/crates/loro-core/src/container/map/tests.rs
index 10572950..d7f67222 100644
--- a/crates/loro-core/src/container/map/tests.rs
+++ b/crates/loro-core/src/container/map/tests.rs
@@ -48,7 +48,7 @@ mod map_proptest {
                 map.insert(k.clone(), v.clone());
                 container.insert(k.clone().into(), v.clone());
                 let snapshot = container.get_value();
-                for (key, value) in snapshot.to_map().unwrap().iter() {
+                for (key, value) in snapshot.as_map().unwrap().iter() {
                     assert_eq!(map.get(&key.to_string()).map(|x|x.clone().into()), Some(value.clone()));
                 }
             }
diff --git a/crates/loro-core/src/container/text/text_content.rs b/crates/loro-core/src/container/text/text_content.rs
index bd28cbef..0c637ea3 100644
--- a/crates/loro-core/src/container/text/text_content.rs
+++ b/crates/loro-core/src/container/text/text_content.rs
@@ -1,4 +1,4 @@
-use crate::{ContentType, InsertContent, ID};
+use crate::{id::Counter, ContentType, InsertContent, ID};
 use rle::{HasLength, Mergable, Sliceable};
 
 #[derive(Debug, Clone)]
@@ -12,9 +12,9 @@ pub struct TextContent {
 impl Mergable for TextContent {
     fn is_mergable(&self, other: &Self, _: &()) -> bool {
         other.id.client_id == self.id.client_id
-            && self.id.counter + self.len() as u32 == other.id.counter
+            && self.id.counter + self.len() as Counter == other.id.counter
             && self.id.client_id == other.origin_left.client_id
-            && self.id.counter + self.len() as u32 - 1 == other.origin_left.counter
+            && self.id.counter + self.len() as Counter - 1 == other.origin_left.counter
             && self.origin_right == other.origin_right
     }
 
@@ -36,12 +36,12 @@ impl Sliceable for TextContent {
             TextContent {
                 origin_left: ID {
                     client_id: self.id.client_id,
-                    counter: self.id.counter + from as u32 - 1,
+                    counter: self.id.counter + from as Counter - 1,
                 },
                 origin_right: self.origin_right,
                 id: ID {
                     client_id: self.id.client_id,
-                    counter: self.id.counter + from as u32,
+                    counter: self.id.counter + from as Counter,
                 },
                 text: self.text[from..to].to_owned(),
             }
diff --git a/crates/loro-core/src/dag.rs b/crates/loro-core/src/dag.rs
index e69de29b..33e45282 100644
--- a/crates/loro-core/src/dag.rs
+++ b/crates/loro-core/src/dag.rs
@@ -0,0 +1,421 @@
+//! DAG (Directed Acyclic Graph) is a common data structure in distributed system.
+//!
+//! This mod contains the DAGs in our CRDT. It's not a general DAG, it has some specific properties that
+//! we used to optimize the speed:
+//! - Each node has lamport clock.
+//! - Each node has its ID (client_id, counter).
+//! - We use ID to refer to node rather than content addressing (hash)
+//!
+use std::{
+    collections::{BinaryHeap, HashMap, HashSet, VecDeque},
+    ops::Range,
+};
+
+use fxhash::{FxHashMap, FxHashSet};
+mod iter;
+mod mermaid;
+#[cfg(test)]
+mod test;
+
+use crate::{
+    change::Lamport,
+    id::{ClientID, Counter, ID},
+    span::{CounterSpan, IdSpan},
+    version::VersionVector,
+};
+
+use self::{
+    iter::{iter_dag, iter_dag_with_vv, DagIterator, DagIteratorVV},
+    mermaid::dag_to_mermaid,
+};
+
+pub(crate) trait DagNode {
+    fn id_start(&self) -> ID;
+    fn lamport_start(&self) -> Lamport;
+    fn len(&self) -> usize;
+    fn deps(&self) -> &Vec<ID>;
+
+    #[inline]
+    fn is_empty(&self) -> bool {
+        self.len() == 0
+    }
+
+    #[inline]
+    fn id_span(&self) -> IdSpan {
+        let id = self.id_start();
+        IdSpan {
+            client_id: id.client_id,
+            counter: CounterSpan::new(id.counter, id.counter + self.len() as Counter),
+        }
+    }
+
+    /// inclusive end
+    #[inline]
+    fn id_end(&self) -> ID {
+        let id = self.id_start();
+        ID {
+            client_id: id.client_id,
+            counter: id.counter + self.len() as Counter - 1,
+        }
+    }
+
+    #[inline]
+    fn get_lamport_from_counter(&self, c: Counter) -> Lamport {
+        self.lamport_start() + c as Lamport - self.id_start().counter as Lamport
+    }
+}
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub(crate) struct Path {
+    retreat: Vec<IdSpan>,
+    forward: Vec<IdSpan>,
+}
+
+#[allow(clippy::ptr_arg)]
+fn reverse_path(path: &mut Vec<IdSpan>) {
+    path.reverse();
+    for span in path.iter_mut() {
+        span.counter.reverse();
+    }
+}
+
+/// Dag (Directed Acyclic Graph).
+///
+/// We have following invariance in DAG
+/// - All deps' lamports are smaller than current node's lamport
+pub(crate) trait Dag {
+    type Node: DagNode;
+
+    fn get(&self, id: ID) -> Option<&Self::Node>;
+
+    #[inline]
+    fn contains(&self, id: ID) -> bool {
+        self.vv().includes(id)
+    }
+
+    fn frontier(&self) -> &[ID];
+    fn roots(&self) -> Vec<&Self::Node>;
+    fn vv(&self) -> VersionVector;
+
+    //
+    // TODO: Maybe use Result return type
+    // TODO: Maybe we only need one heap?
+    // TODO: benchmark
+    // how to test better?
+    // - converge through other nodes
+    //
+    /// only returns a single root.
+    /// but the least common ancestor may be more than one root.
+    /// But that is a rare case.
+    ///
+    #[inline]
+    fn find_common_ancestor(&self, a_id: ID, b_id: ID) -> Option<ID> {
+        find_common_ancestor(
+            &|id| self.get(id).map(|x| x as &dyn DagNode),
+            a_id,
+            b_id,
+            |_, _, _| {},
+        )
+    }
+
+    /// TODO: we probably need cache to speedup this
+    #[inline]
+    fn get_vv(&self, id: ID) -> VersionVector {
+        get_version_vector(&|id| self.get(id).map(|x| x as &dyn DagNode), id)
+    }
+
+    #[inline]
+    fn find_path(&self, from: ID, to: ID) -> Option<Path> {
+        let mut ans: Option<Path> = None;
+
+        fn get_rev_path(target: ID, from: ID, to_from_map: &FxHashMap<ID, ID>) -> Vec<IdSpan> {
+            let mut last_visited: Option<ID> = None;
+            let mut a_rev_path = vec![];
+            let mut node_id = target;
+            node_id = *to_from_map.get(&node_id).unwrap();
+            loop {
+                if let Some(last_id) = last_visited {
+                    if last_id.client_id == node_id.client_id {
+                        debug_assert!(last_id.counter < node_id.counter);
+                        a_rev_path.push(IdSpan {
+                            client_id: last_id.client_id,
+                            counter: CounterSpan::new(last_id.counter, node_id.counter + 1),
+                        });
+                        last_visited = None;
+                    } else {
+                        a_rev_path.push(IdSpan {
+                            client_id: last_id.client_id,
+                            counter: CounterSpan::new(last_id.counter, last_id.counter + 1),
+                        });
+                        last_visited = Some(node_id);
+                    }
+                } else {
+                    last_visited = Some(node_id);
+                }
+
+                if node_id == from {
+                    break;
+                }
+
+                node_id = *to_from_map.get(&node_id).unwrap();
+            }
+
+            if let Some(last_id) = last_visited {
+                a_rev_path.push(IdSpan {
+                    client_id: last_id.client_id,
+                    counter: CounterSpan::new(last_id.counter, last_id.counter + 1),
+                });
+            }
+
+            a_rev_path
+        }
+
+        find_common_ancestor(
+            &|id| self.get(id).map(|x| x as &dyn DagNode),
+            from,
+            to,
+            |ancestor, a_path, b_path| {
+                let mut a_path = get_rev_path(ancestor, from, a_path);
+                let b_path = get_rev_path(ancestor, to, b_path);
+                reverse_path(&mut a_path);
+                ans = Some(Path {
+                    retreat: a_path,
+                    forward: b_path,
+                });
+            },
+        );
+
+        ans
+    }
+
+    fn iter_with_vv(&self) -> DagIteratorVV<'_, Self::Node>
+    where
+        Self: Sized,
+    {
+        iter_dag_with_vv(self)
+    }
+
+    fn iter(&self) -> DagIterator<'_, Self::Node>
+    where
+        Self: Sized,
+    {
+        iter_dag(self)
+    }
+
+    /// You can visualize and generate img link at https://mermaid.live/
+    #[inline]
+    fn mermaid(&self) -> String
+    where
+        Self: Sized,
+    {
+        dag_to_mermaid(self)
+    }
+}
+
+fn get_version_vector<'a, Get>(get: &'a Get, id: ID) -> VersionVector
+where
+    Get: Fn(ID) -> Option<&'a dyn DagNode>,
+{
+    let mut vv = VersionVector::new();
+    let mut visited: FxHashSet<ID> = FxHashSet::default();
+    vv.insert(id.client_id, id.counter + 1);
+    let node = get(id).unwrap();
+
+    if node.deps().is_empty() {
+        return vv;
+    }
+
+    let mut stack = Vec::new();
+    for dep in node.deps() {
+        stack.push(dep);
+    }
+
+    while !stack.is_empty() {
+        let node_id = *stack.pop().unwrap();
+        let node = get(node_id).unwrap();
+        let node_id_start = node.id_start();
+        if !visited.contains(&node_id_start) {
+            vv.try_update_end(node_id);
+            for dep in node.deps() {
+                if !visited.contains(dep) {
+                    stack.push(dep);
+                }
+            }
+
+            visited.insert(node_id_start);
+        }
+    }
+
+    vv
+}
+
+// fn mermaid<T>(dag: &impl Dag<Node = T>) -> String {
+//     dag
+// }
+
+fn find_common_ancestor<'a, F, G>(get: &'a F, a_id: ID, b_id: ID, mut on_found: G) -> Option<ID>
+where
+    F: Fn(ID) -> Option<&'a dyn DagNode>,
+    G: FnMut(ID, &FxHashMap<ID, ID>, &FxHashMap<ID, ID>),
+{
+    if a_id.client_id == b_id.client_id {
+        if a_id.counter <= b_id.counter {
+            Some(a_id)
+        } else {
+            Some(b_id)
+        }
+    } else {
+        #[derive(Debug, PartialEq, Eq)]
+        struct OrdId<'a> {
+            id: ID,
+            lamport: Lamport,
+            deps: &'a [ID],
+        }
+
+        impl<'a> PartialOrd for OrdId<'a> {
+            fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+                Some(self.lamport.cmp(&other.lamport))
+            }
+        }
+
+        impl<'a> Ord for OrdId<'a> {
+            fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+                self.lamport.cmp(&other.lamport)
+            }
+        }
+
+        let mut _a_vv: HashMap<ClientID, Counter, _> = FxHashMap::default();
+        let mut _b_vv: HashMap<ClientID, Counter, _> = FxHashMap::default();
+        // Invariant: every op id inserted to the a_heap is a key in a_path map, except for a_id
+        let mut _a_heap: BinaryHeap<OrdId> = BinaryHeap::new();
+        // Likewise
+        let mut _b_heap: BinaryHeap<OrdId> = BinaryHeap::new();
+        // FxHashMap<To, From> is used to track the deps path of each node
+        let mut _a_path: FxHashMap<ID, ID> = FxHashMap::default();
+        let mut _b_path: FxHashMap<ID, ID> = FxHashMap::default();
+        {
+            let a = get(a_id).unwrap();
+            let b = get(b_id).unwrap();
+            _a_heap.push(OrdId {
+                id: a_id,
+                lamport: a.get_lamport_from_counter(a_id.counter),
+                deps: a.deps(),
+            });
+            _b_heap.push(OrdId {
+                id: b_id,
+                lamport: b.get_lamport_from_counter(b_id.counter),
+                deps: b.deps(),
+            });
+            _a_vv.insert(a_id.client_id, a_id.counter + 1);
+            _b_vv.insert(b_id.client_id, b_id.counter + 1);
+        }
+
+        while !_a_heap.is_empty() || !_b_heap.is_empty() {
+            let (a_heap, b_heap, a_vv, b_vv, a_path, b_path, _swapped) = if _a_heap.is_empty()
+                || (_a_heap.peek().map(|x| x.lamport).unwrap_or(0)
+                    < _b_heap.peek().map(|x| x.lamport).unwrap_or(0))
+            {
+                // swap
+                (
+                    &mut _b_heap,
+                    &mut _a_heap,
+                    &mut _b_vv,
+                    &mut _a_vv,
+                    &mut _b_path,
+                    &mut _a_path,
+                    true,
+                )
+            } else {
+                (
+                    &mut _a_heap,
+                    &mut _b_heap,
+                    &mut _a_vv,
+                    &mut _b_vv,
+                    &mut _a_path,
+                    &mut _b_path,
+                    false,
+                )
+            };
+
+            while !a_heap.is_empty()
+                && a_heap.peek().map(|x| x.lamport).unwrap_or(0)
+                    >= b_heap.peek().map(|x| x.lamport).unwrap_or(0)
+            {
+                let a = a_heap.pop().unwrap();
+                let id = a.id;
+                if let Some(counter_end) = b_vv.get(&id.client_id) {
+                    if id.counter < *counter_end {
+                        b_path
+                            .entry(id)
+                            .or_insert_with(|| ID::new(id.client_id, counter_end - 1));
+
+                        on_found(id, &_a_path, &_b_path);
+                        return Some(id);
+                    }
+                }
+
+                // if swapped {
+                //     println!("A");
+                // } else {
+                //     println!("B");
+                // }
+                // dbg!(&a);
+
+                #[cfg(debug_assertions)]
+                {
+                    if let Some(v) = a_vv.get(&a.id.client_id) {
+                        assert!(*v > a.id.counter)
+                    }
+                }
+
+                for dep_id in a.deps {
+                    if a_path.contains_key(dep_id) {
+                        continue;
+                    }
+
+                    let dep = get(*dep_id).unwrap();
+                    a_heap.push(OrdId {
+                        id: *dep_id,
+                        lamport: dep.get_lamport_from_counter(dep_id.counter),
+                        deps: dep.deps(),
+                    });
+                    a_path.insert(*dep_id, a.id);
+                    if dep.id_start() != *dep_id {
+                        a_path.insert(dep.id_start(), *dep_id);
+                    }
+
+                    if let Some(v) = a_vv.get_mut(&dep_id.client_id) {
+                        if *v < dep_id.counter + 1 {
+                            *v = dep_id.counter + 1;
+                        }
+                    } else {
+                        a_vv.insert(dep_id.client_id, dep_id.counter + 1);
+                    }
+                }
+            }
+        }
+
+        None
+    }
+}
+
+fn update_frontier(frontier: &mut Vec<ID>, new_node_id: ID, new_node_deps: &[ID]) {
+    frontier.retain(|x| {
+        if x.client_id == new_node_id.client_id && x.counter <= new_node_id.counter {
+            return false;
+        }
+
+        !new_node_deps
+            .iter()
+            .any(|y| y.client_id == x.client_id && y.counter >= x.counter)
+    });
+
+    // nodes from the same client with `counter < new_node_id.counter`
+    // are filtered out from frontier.
+    if frontier
+        .iter()
+        .all(|x| x.client_id != new_node_id.client_id)
+    {
+        frontier.push(new_node_id);
+    }
+}
diff --git a/crates/loro-core/src/dag/iter.rs b/crates/loro-core/src/dag/iter.rs
new file mode 100644
index 00000000..63837c09
--- /dev/null
+++ b/crates/loro-core/src/dag/iter.rs
@@ -0,0 +1,175 @@
+use super::*;
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+struct IdHeapItem {
+    id: ID,
+    lamport: Lamport,
+}
+
+impl PartialOrd for IdHeapItem {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.lamport.cmp(&other.lamport).reverse())
+    }
+}
+
+impl Ord for IdHeapItem {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.lamport.cmp(&other.lamport).reverse()
+    }
+}
+
+pub(crate) fn iter_dag_with_vv<T>(dag: &dyn Dag<Node = T>) -> DagIteratorVV<'_, T> {
+    DagIteratorVV {
+        dag,
+        vv_map: Default::default(),
+        visited: VersionVector::new(),
+        heap: BinaryHeap::new(),
+    }
+}
+
+pub(crate) fn iter_dag<T>(dag: &dyn Dag<Node = T>) -> DagIterator<'_, T> {
+    DagIterator {
+        dag,
+        visited: VersionVector::new(),
+        heap: BinaryHeap::new(),
+    }
+}
+
+pub struct DagIterator<'a, T> {
+    dag: &'a dyn Dag<Node = T>,
+    /// Because all deps' lamports are smaller than current node's lamport.
+    /// We can use the lamport to sort the nodes so that each node's deps are processed before itself.
+    ///
+    /// The ids in this heap are start ids of nodes. It won't be a id pointing to the middle of a node.
+    heap: BinaryHeap<IdHeapItem>,
+    visited: VersionVector,
+}
+
+// TODO: Need benchmark on memory
+impl<'a, T: DagNode> Iterator for DagIterator<'a, T> {
+    type Item = &'a T;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.visited.is_empty() {
+            if self.dag.vv().len() == 0 {
+                return None;
+            }
+
+            for (&client_id, _) in self.dag.vv().iter() {
+                if let Some(node) = self.dag.get(ID::new(client_id, 0)) {
+                    self.heap.push(IdHeapItem {
+                        id: ID::new(client_id, 0),
+                        lamport: node.lamport_start(),
+                    });
+                }
+
+                self.visited.insert(client_id, 0);
+            }
+        }
+
+        if !self.heap.is_empty() {
+            let item = self.heap.pop().unwrap();
+            let id = item.id;
+            let node = self.dag.get(id).unwrap();
+            debug_assert_eq!(id, node.id_start());
+
+            // push next node from the same client to the heap
+            let next_id = id.inc(node.len() as i32);
+            if self.dag.contains(next_id) {
+                let next_node = self.dag.get(next_id).unwrap();
+                self.heap.push(IdHeapItem {
+                    id: next_id,
+                    lamport: next_node.lamport_start(),
+                });
+            }
+
+            return Some(node);
+        }
+
+        None
+    }
+}
+
+pub(crate) struct DagIteratorVV<'a, T> {
+    dag: &'a dyn Dag<Node = T>,
+    /// we should keep every nodes starting id inside this map
+    vv_map: FxHashMap<ID, VersionVector>,
+    /// Because all deps' lamports are smaller than current node's lamport.
+    /// We can use the lamport to sort the nodes so that each node's deps are processed before itself.
+    ///
+    /// The ids in this heap are start ids of nodes. It won't be a id pointing to the middle of a node.
+    heap: BinaryHeap<IdHeapItem>,
+    visited: VersionVector,
+}
+
+// TODO: Need benchmark on memory
+impl<'a, T: DagNode> Iterator for DagIteratorVV<'a, T> {
+    type Item = (&'a T, VersionVector);
+
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.vv_map.is_empty() {
+            if self.dag.vv().len() == 0 {
+                return None;
+            }
+
+            for (&client_id, _) in self.dag.vv().iter() {
+                let vv = VersionVector::new();
+                if let Some(node) = self.dag.get(ID::new(client_id, 0)) {
+                    if node.lamport_start() == 0 {
+                        self.vv_map.insert(ID::new(client_id, 0), vv.clone());
+                    }
+
+                    self.heap.push(IdHeapItem {
+                        id: ID::new(client_id, 0),
+                        lamport: node.lamport_start(),
+                    });
+                }
+
+                self.visited.insert(client_id, 0);
+            }
+        }
+
+        if !self.heap.is_empty() {
+            let item = self.heap.pop().unwrap();
+            let id = item.id;
+            let node = self.dag.get(id).unwrap();
+            debug_assert_eq!(id, node.id_start());
+            let mut vv = {
+                // calculate vv
+                let mut vv = None;
+                for &dep_id in node.deps() {
+                    let dep = self.dag.get(dep_id).unwrap();
+                    let dep_vv = self.vv_map.get(&dep.id_start()).unwrap();
+                    if vv.is_none() {
+                        vv = Some(dep_vv.clone());
+                    } else {
+                        vv.as_mut().unwrap().merge(dep_vv);
+                    }
+
+                    if dep.id_start() != dep_id {
+                        vv.as_mut().unwrap().set_end(dep_id);
+                    }
+                }
+
+                vv.unwrap_or_else(VersionVector::new)
+            };
+
+            vv.try_update_end(id);
+            self.vv_map.insert(node.id_start(), vv.clone());
+
+            // push next node from the same client to the heap
+            let next_id = id.inc(node.len() as i32);
+            if self.dag.contains(next_id) {
+                let next_node = self.dag.get(next_id).unwrap();
+                self.heap.push(IdHeapItem {
+                    id: next_id,
+                    lamport: next_node.lamport_start(),
+                });
+            }
+
+            return Some((node, vv));
+        }
+
+        None
+    }
+}
diff --git a/crates/loro-core/src/dag/mermaid.rs b/crates/loro-core/src/dag/mermaid.rs
new file mode 100644
index 00000000..ea28606a
--- /dev/null
+++ b/crates/loro-core/src/dag/mermaid.rs
@@ -0,0 +1,143 @@
+use rle::RleVec;
+
+use super::*;
+struct BreakPoints {
+    vv: VersionVector,
+    break_points: FxHashMap<ClientID, FxHashSet<Counter>>,
+    /// start ID to ID. The target ID may be in the middle of an op.
+    ///
+    /// only includes links across different clients
+    links: FxHashMap<ID, ID>,
+}
+
+struct Output {
+    clients: FxHashMap<ClientID, Vec<IdSpan>>,
+    /// start ID to start ID.
+    ///
+    /// only includes links across different clients
+    links: FxHashMap<ID, ID>,
+}
+
+fn to_str(output: Output) -> String {
+    let mut s = String::new();
+    let mut indent_level = 0;
+    macro_rules! new_line {
+        () => {
+            s += "\n";
+            for _ in 0..indent_level {
+                s += "    ";
+            }
+        };
+    }
+    s += "flowchart RL";
+    indent_level += 1;
+    new_line!();
+    for (client_id, spans) in output.clients.iter() {
+        s += format!("subgraph client{}", client_id).as_str();
+        new_line!();
+        let mut is_first = true;
+        for id_span in spans.iter().rev() {
+            if !is_first {
+                s += " --> "
+            }
+
+            is_first = false;
+            s += format!(
+                "{}-{}(\"c{}: [{}, {})\")",
+                id_span.client_id,
+                id_span.counter.from,
+                id_span.client_id,
+                id_span.counter.from,
+                id_span.counter.to
+            )
+            .as_str();
+        }
+
+        new_line!();
+        s += "end";
+        new_line!();
+        new_line!();
+    }
+
+    for (id_from, id_to) in output.links.iter() {
+        s += format!(
+            "{}-{} --> {}-{}",
+            id_from.client_id, id_from.counter, id_to.client_id, id_to.counter
+        )
+        .as_str();
+        new_line!();
+    }
+
+    s
+}
+
+fn break_points_to_output(input: BreakPoints) -> Output {
+    let mut output = Output {
+        clients: FxHashMap::default(),
+        links: FxHashMap::default(),
+    };
+    let breaks: FxHashMap<ClientID, Vec<Counter>> = input
+        .break_points
+        .into_iter()
+        .map(|(client_id, set)| {
+            let mut vec: Vec<Counter> = set.iter().cloned().collect();
+            vec.sort();
+            (client_id, vec)
+        })
+        .collect();
+    for (client_id, break_points) in breaks.iter() {
+        let mut spans = vec![];
+        for (from, to) in break_points.iter().zip(break_points.iter().skip(1)) {
+            spans.push(IdSpan::new(*client_id, *from, *to));
+        }
+        output.clients.insert(*client_id, spans);
+    }
+
+    for (id_from, id_to) in input.links.iter() {
+        let client_breaks = breaks.get(&id_to.client_id).unwrap();
+        match client_breaks.binary_search(&id_to.counter) {
+            Ok(_) => {
+                output.links.insert(*id_from, *id_to);
+            }
+            Err(index) => {
+                output
+                    .links
+                    .insert(*id_from, ID::new(id_to.client_id, client_breaks[index - 1]));
+            }
+        }
+    }
+    output
+}
+
+fn get_dag_break_points<T: DagNode>(dag: &impl Dag<Node = T>) -> BreakPoints {
+    let mut break_points = BreakPoints {
+        vv: dag.vv(),
+        break_points: FxHashMap::default(),
+        links: FxHashMap::default(),
+    };
+
+    for node in dag.iter() {
+        let id = node.id_start();
+        let set = break_points.break_points.entry(id.client_id).or_default();
+        set.insert(id.counter);
+        set.insert(id.counter + node.len() as Counter);
+        for dep in node.deps() {
+            if dep.client_id == id.client_id {
+                continue;
+            }
+
+            break_points
+                .break_points
+                .entry(dep.client_id)
+                .or_default()
+                .insert(dep.counter);
+            break_points.links.insert(id, *dep);
+        }
+    }
+
+    break_points
+}
+
+pub(crate) fn dag_to_mermaid<T: DagNode>(dag: &impl Dag<Node = T>) -> String {
+    to_str(break_points_to_output(get_dag_break_points(dag)))
+}
diff --git a/crates/loro-core/src/dag/test.rs b/crates/loro-core/src/dag/test.rs
new file mode 100644
index 00000000..42507ab0
--- /dev/null
+++ b/crates/loro-core/src/dag/test.rs
@@ -0,0 +1,635 @@
+#![cfg(test)]
+
+use proptest::proptest;
+
+use super::*;
+use crate::{
+    array_mut_ref,
+    change::Lamport,
+    id::{ClientID, Counter, ID},
+    span::{CounterSpan, IdSpan},
+};
+use std::collections::HashSet;
+use std::iter::FromIterator;
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+struct TestNode {
+    id: ID,
+    lamport: Lamport,
+    len: usize,
+    deps: Vec<ID>,
+}
+
+impl TestNode {
+    fn new(id: ID, lamport: Lamport, deps: Vec<ID>, len: usize) -> Self {
+        Self {
+            id,
+            lamport,
+            deps,
+            len,
+        }
+    }
+}
+
+impl DagNode for TestNode {
+    fn id_start(&self) -> ID {
+        self.id
+    }
+    fn lamport_start(&self) -> Lamport {
+        self.lamport
+    }
+    fn len(&self) -> usize {
+        self.len
+    }
+    fn deps(&self) -> &Vec<ID> {
+        &self.deps
+    }
+}
+
+#[derive(Debug, PartialEq, Eq)]
+struct TestDag {
+    nodes: FxHashMap<ClientID, Vec<TestNode>>,
+    frontier: Vec<ID>,
+    version_vec: VersionVector,
+    next_lamport: Lamport,
+    client_id: ClientID,
+}
+
+impl Dag for TestDag {
+    type Node = TestNode;
+
+    fn get(&self, id: ID) -> Option<&Self::Node> {
+        self.nodes.get(&id.client_id)?.iter().find(|node| {
+            id.counter >= node.id.counter && id.counter < node.id.counter + node.len as Counter
+        })
+    }
+
+    fn frontier(&self) -> &[ID] {
+        &self.frontier
+    }
+
+    fn roots(&self) -> Vec<&Self::Node> {
+        self.nodes.iter().map(|(_, v)| &v[0]).collect()
+    }
+
+    fn contains(&self, id: ID) -> bool {
+        self.version_vec
+            .get(&id.client_id)
+            .and_then(|x| if *x > id.counter { Some(()) } else { None })
+            .is_some()
+    }
+
+    fn vv(&self) -> VersionVector {
+        self.version_vec.clone()
+    }
+}
+
+impl TestDag {
+    pub fn new(client_id: ClientID) -> Self {
+        Self {
+            nodes: FxHashMap::default(),
+            frontier: Vec::new(),
+            version_vec: VersionVector::new(),
+            next_lamport: 0,
+            client_id,
+        }
+    }
+
+    fn get_last_node(&mut self) -> &mut TestNode {
+        self.nodes
+            .get_mut(&self.client_id)
+            .unwrap()
+            .last_mut()
+            .unwrap()
+    }
+
+    fn push(&mut self, len: usize) {
+        let client_id = self.client_id;
+        let counter = self.version_vec.entry(client_id).or_insert(0);
+        let id = ID::new(client_id, *counter);
+        *counter += len as Counter;
+        let deps = std::mem::replace(&mut self.frontier, vec![id]);
+        self.nodes
+            .entry(client_id)
+            .or_insert(vec![])
+            .push(TestNode::new(id, self.next_lamport, deps, len));
+        self.next_lamport += len as u32;
+    }
+
+    fn merge(&mut self, other: &TestDag) {
+        let mut pending = Vec::new();
+        for (_, nodes) in other.nodes.iter() {
+            for (i, node) in nodes.iter().enumerate() {
+                if self._try_push_node(node, &mut pending, i) {
+                    break;
+                }
+            }
+        }
+
+        let mut current = pending;
+        let mut pending = Vec::new();
+        while !pending.is_empty() || !current.is_empty() {
+            if current.is_empty() {
+                std::mem::swap(&mut pending, &mut current);
+            }
+
+            let (client_id, index) = current.pop().unwrap();
+            let node_vec = other.nodes.get(&client_id).unwrap();
+            #[allow(clippy::needless_range_loop)]
+            for i in index..node_vec.len() {
+                let node = &node_vec[i];
+                if self._try_push_node(node, &mut pending, i) {
+                    break;
+                }
+            }
+        }
+    }
+
+    fn _try_push_node(
+        &mut self,
+        node: &TestNode,
+        pending: &mut Vec<(u64, usize)>,
+        i: usize,
+    ) -> bool {
+        let client_id = node.id.client_id;
+        if self.contains(node.id) {
+            return false;
+        }
+        if node.deps.iter().any(|dep| !self.contains(*dep)) {
+            pending.push((client_id, i));
+            return true;
+        }
+        update_frontier(
+            &mut self.frontier,
+            node.id.inc((node.len() - 1) as Counter),
+            &node.deps,
+        );
+        self.nodes
+            .entry(client_id)
+            .or_insert(vec![])
+            .push(node.clone());
+        self.version_vec
+            .insert(client_id, node.id.counter + node.len as Counter);
+        self.next_lamport = self.next_lamport.max(node.lamport + node.len as u32);
+        false
+    }
+}
+
+#[test]
+fn test_dag() {
+    let mut a = TestDag::new(0);
+    let mut b = TestDag::new(1);
+    a.push(1);
+    assert_eq!(a.frontier().len(), 1);
+    assert_eq!(a.frontier()[0].counter, 0);
+    b.push(1);
+    a.merge(&b);
+    assert_eq!(a.frontier().len(), 2);
+    a.push(1);
+    assert_eq!(a.frontier().len(), 1);
+    // a:   0 --(merge)--- 1
+    //            ↑
+    //            |
+    // b:   0 ----
+    assert_eq!(
+        a.frontier()[0],
+        ID {
+            client_id: 0,
+            counter: 1
+        }
+    );
+
+    // a:   0 --(merge)--- 1 --- 2 -------
+    //            ↑                      |
+    //            |                     ↓
+    // b:   0 ------------1----------(merge)
+    a.push(1);
+    b.push(1);
+    b.merge(&a);
+    assert_eq!(b.next_lamport, 3);
+    assert_eq!(b.frontier().len(), 2);
+    assert_eq!(
+        b.find_common_ancestor(ID::new(0, 2), ID::new(1, 1)),
+        Some(ID::new(1, 0))
+    );
+}
+
+#[derive(Debug, Clone, Copy)]
+struct Interaction {
+    dag_idx: usize,
+    merge_with: Option<usize>,
+    len: usize,
+}
+
+impl Interaction {
+    fn gen(rng: &mut impl rand::Rng, num: usize) -> Self {
+        if rng.gen_bool(0.5) {
+            let dag_idx = rng.gen_range(0..num);
+            let merge_with = (rng.gen_range(1..num - 1) + dag_idx) % num;
+            Self {
+                dag_idx,
+                merge_with: Some(merge_with),
+                len: rng.gen_range(1..10),
+            }
+        } else {
+            Self {
+                dag_idx: rng.gen_range(0..num),
+                merge_with: None,
+                len: rng.gen_range(1..10),
+            }
+        }
+    }
+
+    fn apply(&self, dags: &mut [TestDag]) {
+        if let Some(merge_with) = self.merge_with {
+            if merge_with != self.dag_idx {
+                let (from, to) = array_mut_ref!(dags, [self.dag_idx, merge_with]);
+                from.merge(to);
+            }
+        }
+
+        dags[self.dag_idx].push(self.len);
+    }
+}
+
+mod iter {
+    use super::*;
+
+    #[test]
+    fn test() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        // 0-0
+        a.push(1);
+        // 1-0
+        b.push(1);
+        a.merge(&b);
+        // 0-1
+        a.push(1);
+        b.merge(&a);
+        // 1-1
+        b.push(1);
+        a.merge(&b);
+        // 0-2
+        a.push(1);
+
+        let mut count = 0;
+        for (node, vv) in a.iter_with_vv() {
+            count += 1;
+            if node.id == ID::new(0, 0) {
+                assert_eq!(vv, vec![ID::new(0, 0)].into());
+            } else if node.id == ID::new(0, 2) {
+                assert_eq!(vv, vec![ID::new(0, 2), ID::new(1, 1)].into());
+            }
+        }
+
+        assert_eq!(count, 5);
+    }
+}
+
+mod mermaid {
+    use rle::Mergable;
+
+    use super::*;
+
+    #[test]
+    fn simple() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        // 0-0
+        a.push(1);
+        // 1-0
+        b.push(1);
+        a.merge(&b);
+        // 0-1
+        a.push(1);
+        b.merge(&a);
+        // 1-1
+        b.push(1);
+        a.merge(&b);
+        // 0-2
+        a.push(1);
+
+        println!("{}", a.mermaid());
+    }
+
+    #[test]
+    fn three() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        let mut c = TestDag::new(2);
+        a.push(10);
+        b.merge(&a);
+        b.push(3);
+        c.merge(&b);
+        c.push(4);
+        a.merge(&c);
+        a.push(2);
+        b.merge(&a);
+        println!("{}", b.mermaid());
+    }
+
+    #[test]
+    fn gen() {
+        let num = 5;
+        let mut rng = rand::thread_rng();
+        let mut dags = (0..num).map(TestDag::new).collect::<Vec<_>>();
+        for _ in 0..100 {
+            Interaction::gen(&mut rng, num as usize).apply(&mut dags);
+        }
+        for i in 1..num {
+            let (a, other) = array_mut_ref!(&mut dags, [0, i as usize]);
+            a.merge(other);
+        }
+        println!("{}", dags[0].mermaid());
+    }
+}
+
+mod get_version_vector {
+    use super::*;
+
+    #[test]
+    fn vv() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        a.push(1);
+        b.push(1);
+        a.merge(&b);
+        a.push(1);
+        let actual = a.get_vv(ID::new(0, 0));
+        assert_eq!(actual, vec![ID::new(0, 0)].into());
+        let actual = a.get_vv(ID::new(0, 1));
+        assert_eq!(actual, vec![ID::new(0, 1), ID::new(1, 0)].into());
+
+        let mut c = TestDag::new(2);
+        c.merge(&a);
+        b.push(1);
+        c.merge(&b);
+        c.push(1);
+        let actual = c.get_vv(ID::new(2, 0));
+        assert_eq!(
+            actual,
+            vec![ID::new(0, 1), ID::new(1, 1), ID::new(2, 0)].into()
+        );
+    }
+}
+
+mod find_path {
+    use super::*;
+
+    #[test]
+    fn no_path() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        a.push(1);
+        b.push(1);
+        a.merge(&b);
+        let actual = a.find_path(ID::new(0, 0), ID::new(1, 0));
+        assert_eq!(actual, None);
+    }
+
+    #[test]
+    fn one_path() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        // 0 - 0
+        a.push(1);
+        b.merge(&a);
+        // 1 - 0
+        b.push(1);
+        // 0 - 1
+        a.push(1);
+        a.merge(&b);
+        let actual = a.find_path(ID::new(0, 1), ID::new(1, 0));
+        assert_eq!(
+            actual,
+            Some(Path {
+                retreat: vec![IdSpan::new(0, 1, 0)],
+                forward: vec![IdSpan::new(1, 0, 1)],
+            })
+        );
+    }
+
+    #[test]
+    fn middle() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        a.push(4);
+        b.push(1);
+        b.push(1);
+        let node = b.get_last_node();
+        node.deps.push(ID::new(0, 2));
+        b.merge(&a);
+        let actual = b.find_path(ID::new(0, 3), ID::new(1, 1));
+        assert_eq!(
+            actual,
+            Some(Path {
+                retreat: vec![IdSpan::new(0, 3, 2)],
+                forward: vec![IdSpan::new(1, 1, 2)],
+            })
+        );
+    }
+}
+
+mod find_common_ancestors {
+    use super::*;
+
+    #[test]
+    fn no_common_ancestors() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        a.push(1);
+        b.push(1);
+        a.merge(&b);
+        let actual = a.find_common_ancestor(ID::new(0, 0), ID::new(1, 0));
+        assert_eq!(actual, None);
+
+        // interactions between b and c
+        let mut c = TestDag::new(2);
+        c.merge(&b);
+        c.push(2);
+        b.merge(&c);
+        b.push(3);
+
+        // should no exist any common ancestor between a and b
+        let actual = a.find_common_ancestor(ID::new(0, 0), ID::new(1, 0));
+        assert_eq!(actual, None);
+    }
+
+    #[test]
+    fn dep_in_middle() {
+        let mut a = TestDag::new(0);
+        let mut b = TestDag::new(1);
+        a.push(4);
+        b.push(4);
+        b.push(5);
+        b.merge(&a);
+        b.frontier.retain(|x| x.client_id == 1);
+        let k = b.nodes.get_mut(&1).unwrap();
+        k[1].deps.push(ID::new(0, 2));
+        assert_eq!(
+            b.find_common_ancestor(ID::new(0, 3), ID::new(1, 8)),
+            Some(ID::new(0, 2))
+        );
+    }
+
+    /// ![](https://mermaid.ink/img/pako:eNqNkTFPwzAQhf_K6SYqOZJ9CYsHJroxwYgXY7skInEq1xFCVf87jg5XVQQSnk6fz_feO5_RzT6gxsM4f7repgzPTyZCOafl7T3ZYw9uHELMkqls2juDTmp4bQV0O4M7aJqHwqlyEtDecFW5EkA3XFYuBaiVs0CInotfXSimqunW16q87gTcX6cqdqe27hSrKVZr_6tGTImn0nYqcWbaZiZWI1ajP9WK2zqnClFd5jVn3SIKnEKa7ODLb53Xa4O5D1MwqEvpbfowaOKl9C1Hb3PY-yHPCfXBjqcg0C55fvmKDnVOS6hNj4Mtgaefrss3dp6HFg)
+    #[test]
+    fn large_lamport_with_longer_path() {
+        let mut a0 = TestDag::new(0);
+        let mut a1 = TestDag::new(1);
+        let mut a2 = TestDag::new(2);
+
+        a0.push(3);
+        a1.push(3);
+        a2.push(2);
+        a2.merge(&a0);
+        a2.push(1);
+        a1.merge(&a2);
+        a2.push(1);
+        a1.push(1);
+        a1.merge(&a2);
+        a1.push(1);
+        a1.nodes
+            .get_mut(&1)
+            .unwrap()
+            .last_mut()
+            .unwrap()
+            .deps
+            .push(ID::new(0, 1));
+        a0.push(1);
+        a1.merge(&a2);
+        a1.merge(&a0);
+        assert_eq!(
+            a1.find_common_ancestor(ID::new(0, 3), ID::new(1, 4)),
+            Some(ID::new(0, 2))
+        );
+    }
+}
+
+#[cfg(not(no_proptest))]
+mod find_common_ancestors_proptest {
+    use proptest::prelude::*;
+
+    use crate::{array_mut_ref, unsafe_array_mut_ref};
+
+    use super::*;
+
+    prop_compose! {
+        fn gen_interaction(num: usize) (
+                dag_idx in 0..num,
+                merge_with in 0..num,
+                length in 1..10,
+                should_merge in 0..2
+            ) -> Interaction {
+            Interaction {
+                dag_idx,
+                merge_with: if should_merge == 1 && merge_with != dag_idx { Some(merge_with) } else { None },
+                len: length as usize,
+            }
+        }
+    }
+
+    proptest! {
+        #[test]
+        fn test_2dags(
+            before_merged_insertions in prop::collection::vec(gen_interaction(2), 0..300),
+            after_merged_insertions in prop::collection::vec(gen_interaction(2), 0..300)
+        ) {
+            test(2, before_merged_insertions, after_merged_insertions)?;
+        }
+
+        #[test]
+        fn test_4dags(
+            before_merged_insertions in prop::collection::vec(gen_interaction(4), 0..300),
+            after_merged_insertions in prop::collection::vec(gen_interaction(4), 0..300)
+        ) {
+            test(4, before_merged_insertions, after_merged_insertions)?;
+        }
+
+        #[test]
+        fn test_10dags(
+            before_merged_insertions in prop::collection::vec(gen_interaction(10), 0..300),
+            after_merged_insertions in prop::collection::vec(gen_interaction(10), 0..300)
+        ) {
+            test(10, before_merged_insertions, after_merged_insertions)?;
+        }
+    }
+
+    fn preprocess(interactions: &mut [Interaction], num: i32) {
+        for interaction in interactions.iter_mut() {
+            interaction.dag_idx %= num as usize;
+            if let Some(ref mut merge_with) = interaction.merge_with {
+                *merge_with %= num as usize;
+                if *merge_with == interaction.dag_idx {
+                    *merge_with = (*merge_with + 1) % num as usize;
+                }
+            }
+        }
+    }
+
+    fn test(
+        dag_num: i32,
+        mut before_merge_insertion: Vec<Interaction>,
+        mut after_merge_insertion: Vec<Interaction>,
+    ) -> Result<(), TestCaseError> {
+        preprocess(&mut before_merge_insertion, dag_num);
+        preprocess(&mut after_merge_insertion, dag_num);
+        let mut dags = Vec::new();
+        for i in 0..dag_num {
+            dags.push(TestDag::new(i as ClientID));
+        }
+
+        for interaction in before_merge_insertion {
+            apply(interaction, &mut dags);
+        }
+
+        let (dag0,): (&mut TestDag,) = unsafe_array_mut_ref!(&mut dags, [0]);
+        for dag in &dags[1..] {
+            dag0.merge(dag);
+        }
+
+        dag0.push(1);
+        let expected = dag0.frontier()[0];
+        for dag in &mut dags[1..] {
+            dag.merge(dag0);
+        }
+        for interaction in after_merge_insertion.iter_mut() {
+            if let Some(merge) = interaction.merge_with {
+                // odd dag merges with the odd
+                // even dag merges with the even
+                if merge % 2 != interaction.dag_idx % 2 {
+                    interaction.merge_with = None;
+                }
+            }
+
+            apply(*interaction, &mut dags);
+        }
+
+        let (dag0, dag1) = array_mut_ref!(&mut dags, [0, 1]);
+        dag1.push(1);
+        dag0.merge(dag1);
+        // dbg!(dag0, dag1, expected);
+        let a = dags[0].nodes.get(&0).unwrap().last().unwrap().id;
+        let b = dags[1].nodes.get(&1).unwrap().last().unwrap().id;
+        let actual = dags[0].find_common_ancestor(a, b);
+        prop_assert_eq!(actual.unwrap(), expected);
+        Ok(())
+    }
+
+    fn apply(interaction: Interaction, dags: &mut [TestDag]) {
+        let Interaction {
+            dag_idx,
+            len,
+            merge_with,
+        } = interaction;
+        if let Some(merge_with) = merge_with {
+            let (dag, merge_target): (&mut TestDag, &mut TestDag) =
+                array_mut_ref!(dags, [dag_idx, merge_with]);
+            dag.push(len);
+            dag.merge(merge_target);
+        } else {
+            dags[dag_idx].push(len);
+        }
+    }
+}
diff --git a/crates/loro-core/src/id.rs b/crates/loro-core/src/id.rs
index f2d446e7..ec8e9188 100644
--- a/crates/loro-core/src/id.rs
+++ b/crates/loro-core/src/id.rs
@@ -1,21 +1,21 @@
 use serde::Serialize;
 
 pub type ClientID = u64;
-pub type Counter = u32;
+pub type Counter = i32;
 
 #[derive(PartialEq, Eq, Hash, Clone, Debug, Copy, PartialOrd, Ord, Serialize)]
 pub struct ID {
     pub client_id: u64,
-    pub counter: u32,
+    pub counter: Counter,
 }
 
 pub const ROOT_ID: ID = ID {
     client_id: u64::MAX,
-    counter: u32::MAX,
+    counter: i32::MAX,
 };
 
 impl ID {
-    pub fn new(client_id: u64, counter: u32) -> Self {
+    pub fn new(client_id: u64, counter: Counter) -> Self {
         ID { client_id, counter }
     }
 
@@ -28,11 +28,11 @@ impl ID {
     }
 
     #[inline]
-    pub(crate) fn is_connected_id(&self, other: &Self, self_len: u32) -> bool {
-        self.client_id == other.client_id && self.counter + self_len == other.counter
+    pub(crate) fn is_connected_id(&self, other: &Self, self_len: usize) -> bool {
+        self.client_id == other.client_id && self.counter + self_len as Counter == other.counter
     }
 
-    pub fn inc(&self, inc: u32) -> Self {
+    pub fn inc(&self, inc: i32) -> Self {
         ID {
             client_id: self.client_id,
             counter: self.counter + inc,
diff --git a/crates/loro-core/src/lib.rs b/crates/loro-core/src/lib.rs
index b8c91195..b695e772 100644
--- a/crates/loro-core/src/lib.rs
+++ b/crates/loro-core/src/lib.rs
@@ -1,22 +1,24 @@
-//! # Loro
+//! loro-core is a CRDT framework.
 //!
 //!
-#![allow(dead_code, unused_imports, clippy::explicit_auto_deref)]
+//!
+#![allow(dead_code, unused_imports)]
 
 pub mod change;
 pub mod configure;
 pub mod container;
 pub mod dag;
 pub mod id;
+pub mod log_store;
 pub mod op;
 pub mod version;
 
 mod error;
-mod log_store;
 mod loro;
 mod smstring;
 mod snapshot;
 mod span;
+#[cfg(test)]
 mod tests;
 mod value;
 
@@ -31,5 +33,6 @@ pub use container::ContainerType;
 pub use log_store::LogStore;
 pub use loro::*;
 pub use value::LoroValue;
+pub use version::VersionVector;
 
 use string_cache::DefaultAtom;
diff --git a/crates/loro-core/src/log_store.rs b/crates/loro-core/src/log_store.rs
index 453e9388..3f646e17 100644
--- a/crates/loro-core/src/log_store.rs
+++ b/crates/loro-core/src/log_store.rs
@@ -1,3 +1,6 @@
+//! [LogStore] stores all the [Change]s and [Op]s. It's also a [DAG][crate::dag];
+//!
+//!
 mod iter;
 use pin_project::pin_project;
 use std::{collections::BinaryHeap, marker::PhantomPinned, pin::Pin, ptr::NonNull};
@@ -38,6 +41,8 @@ impl Default for GcConfig {
 
 /// Entry of the loro inner state.
 /// This is a self-referential structure. So it need to be pinned.
+///
+/// `frontier`s are the Changes without children in the DAG (there is no dep pointing to them)
 #[pin_project]
 pub struct LogStore {
     changes: FxHashMap<ClientID, RleVec<Change, ChangeMergeCfg>>,
diff --git a/crates/loro-core/src/log_store/iter.rs b/crates/loro-core/src/log_store/iter.rs
index 557cf15a..351a9fd5 100644
--- a/crates/loro-core/src/log_store/iter.rs
+++ b/crates/loro-core/src/log_store/iter.rs
@@ -61,7 +61,7 @@ impl<'a> Iterator for OpIter<'a> {
                         self.heap.push(Reverse(OpProxy::new(
                             change,
                             op,
-                            Some(start..(op.len() as u32)),
+                            Some(start..(op.len() as Counter)),
                         )));
                     }
                 }
diff --git a/crates/loro-core/src/macros.rs b/crates/loro-core/src/macros.rs
index 21e3ad69..e7994ed9 100644
--- a/crates/loro-core/src/macros.rs
+++ b/crates/loro-core/src/macros.rs
@@ -20,3 +20,68 @@ macro_rules! fx_map {
         }
     };
 }
+
+#[macro_export]
+macro_rules! unsafe_array_mut_ref {
+    ($arr:expr, [$($idx:expr),*]) => {
+        {
+            unsafe {
+                (
+                    $(
+                        {  &mut *(&mut $arr[$idx] as *mut _) }
+                    ),*,
+                )
+            }
+        }
+    }
+}
+
+#[macro_export]
+macro_rules! array_mut_ref {
+    ($arr:expr, [$a0:expr, $a1:expr]) => {{
+        #[inline]
+        fn borrow_mut_ref<T>(arr: &mut [T], a0: usize, a1: usize) -> (&mut T, &mut T) {
+            debug_assert!(a0 != a1);
+            unsafe {
+                (
+                    &mut *(&mut arr[a0] as *mut _),
+                    &mut *(&mut arr[a1] as *mut _),
+                )
+            }
+        }
+
+        borrow_mut_ref($arr, $a0, $a1)
+    }};
+    ($arr:expr, [$a0:expr, $a1:expr, $a2:expr]) => {{
+        #[inline]
+        fn borrow_mut_ref<T>(
+            arr: &mut [T],
+            a0: usize,
+            a1: usize,
+            a2: usize,
+        ) -> (&mut T, &mut T, &mut T) {
+            debug_assert!(a0 != a1 && a1 != a2 && a0 != a2);
+            unsafe {
+                (
+                    &mut *(&mut arr[a0] as *mut _),
+                    &mut *(&mut arr[a1] as *mut _),
+                    &mut *(&mut arr[a2] as *mut _),
+                )
+            }
+        }
+
+        borrow_mut_ref($arr, $a0, $a1, $a2)
+    }};
+}
+
+#[test]
+fn test_macro() {
+    let mut arr = vec![100, 101, 102, 103];
+    let (a, b, c) = array_mut_ref!(&mut arr, [1, 2, 3]);
+    assert_eq!(*a, 101);
+    assert_eq!(*b, 102);
+    *a = 50;
+    *b = 51;
+    assert!(arr[1] == 50);
+    assert!(arr[2] == 51);
+}
diff --git a/crates/loro-core/src/op.rs b/crates/loro-core/src/op.rs
index 7d6712f0..1bca4ae9 100644
--- a/crates/loro-core/src/op.rs
+++ b/crates/loro-core/src/op.rs
@@ -1,6 +1,6 @@
 use crate::{
     container::ContainerID,
-    id::ID,
+    id::{Counter, ID},
     span::{CounterSpan, IdSpan},
 };
 use rle::{HasLength, Mergable, RleVec, Sliceable};
@@ -78,7 +78,7 @@ impl Op {
 
 impl Mergable for Op {
     fn is_mergable(&self, other: &Self, cfg: &()) -> bool {
-        self.id.is_connected_id(&other.id, self.len() as u32)
+        self.id.is_connected_id(&other.id, self.len())
             && self.content.is_mergable(&other.content, cfg)
             && self.container == other.container
     }
@@ -124,7 +124,7 @@ impl Sliceable for Op {
         Op {
             id: ID {
                 client_id: self.id.client_id,
-                counter: (self.id.counter + from as u32),
+                counter: (self.id.counter + from as Counter),
             },
             content,
             container: self.container.clone(),
diff --git a/crates/loro-core/src/op/op_proxy.rs b/crates/loro-core/src/op/op_proxy.rs
index 9c999dc5..3be68e02 100644
--- a/crates/loro-core/src/op/op_proxy.rs
+++ b/crates/loro-core/src/op/op_proxy.rs
@@ -2,14 +2,16 @@ use std::ops::Range;
 
 use rle::{HasLength, Sliceable};
 
-use crate::{container::ContainerID, Change, Lamport, Op, OpContent, OpType, Timestamp, ID};
+use crate::{
+    container::ContainerID, id::Counter, Change, Lamport, Op, OpContent, OpType, Timestamp, ID,
+};
 
 /// OpProxy represents a slice of an Op
 pub struct OpProxy<'a> {
     change: &'a Change,
     op: &'a Op,
     /// slice range of the op, op[slice_range]
-    slice_range: Range<u32>,
+    slice_range: Range<Counter>,
 }
 
 impl PartialEq for OpProxy<'_> {
@@ -43,20 +45,21 @@ impl Ord for OpProxy<'_> {
 }
 
 impl<'a> OpProxy<'a> {
-    pub fn new(change: &'a Change, op: &'a Op, range: Option<Range<u32>>) -> Self {
+    pub fn new(change: &'a Change, op: &'a Op, range: Option<Range<Counter>>) -> Self {
         OpProxy {
             change,
             op,
             slice_range: if let Some(range) = range {
                 range
             } else {
-                0..op.len() as u32
+                0..op.len() as Counter
             },
         }
     }
 
     pub fn lamport(&self) -> Lamport {
-        self.change.lamport + self.op.id.counter - self.change.id.counter + self.slice_range.start
+        self.change.lamport + self.op.id.counter as Lamport - self.change.id.counter as Lamport
+            + self.slice_range.start as Lamport
     }
 
     pub fn id(&self) -> ID {
@@ -74,7 +77,7 @@ impl<'a> OpProxy<'a> {
         self.op
     }
 
-    pub fn slice_range(&self) -> &Range<u32> {
+    pub fn slice_range(&self) -> &Range<Counter> {
         &self.slice_range
     }
 
diff --git a/crates/loro-core/src/span.rs b/crates/loro-core/src/span.rs
index 966bf20d..eee9891a 100644
--- a/crates/loro-core/src/span.rs
+++ b/crates/loro-core/src/span.rs
@@ -13,6 +13,19 @@ impl CounterSpan {
         CounterSpan { from, to }
     }
 
+    #[inline]
+    pub fn reverse(&mut self) {
+        if self.from == self.to {
+            return;
+        }
+
+        if self.from < self.to {
+            (self.from, self.to) = (self.to - 1, self.from - 1);
+        } else {
+            (self.from, self.to) = (self.to + 1, self.from + 1);
+        }
+    }
+
     #[inline]
     pub fn min(&self) -> Counter {
         if self.from < self.to {
@@ -81,6 +94,14 @@ pub struct IdSpan {
 }
 
 impl IdSpan {
+    #[inline]
+    pub fn new(client_id: ClientID, from: Counter, to: Counter) -> Self {
+        Self {
+            client_id,
+            counter: CounterSpan { from, to },
+        }
+    }
+
     #[inline]
     pub fn min(&self) -> Counter {
         self.counter.min()
diff --git a/crates/loro-core/src/value.rs b/crates/loro-core/src/value.rs
index a1af55b9..a37145ea 100644
--- a/crates/loro-core/src/value.rs
+++ b/crates/loro-core/src/value.rs
@@ -96,7 +96,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_map(&self) -> Option<&FxHashMap<InternalString, LoroValue>> {
+    pub fn as_map(&self) -> Option<&FxHashMap<InternalString, LoroValue>> {
         match self {
             LoroValue::Map(m) => Some(m),
             _ => None,
@@ -104,7 +104,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_list(&self) -> Option<&Vec<LoroValue>> {
+    pub fn as_list(&self) -> Option<&Vec<LoroValue>> {
         match self {
             LoroValue::List(l) => Some(l),
             _ => None,
@@ -112,7 +112,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_string(&self) -> Option<&SmString> {
+    pub fn as_string(&self) -> Option<&SmString> {
         match self {
             LoroValue::String(s) => Some(s),
             _ => None,
@@ -120,7 +120,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_integer(&self) -> Option<i32> {
+    pub fn as_integer(&self) -> Option<i32> {
         match self {
             LoroValue::Integer(i) => Some(*i),
             _ => None,
@@ -128,7 +128,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_double(&self) -> Option<f64> {
+    pub fn as_double(&self) -> Option<f64> {
         match self {
             LoroValue::Double(d) => Some(*d),
             _ => None,
@@ -136,7 +136,7 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_bool(&self) -> Option<bool> {
+    pub fn as_bool(&self) -> Option<bool> {
         match self {
             LoroValue::Bool(b) => Some(*b),
             _ => None,
@@ -144,7 +144,63 @@ impl LoroValue {
     }
 
     #[inline]
-    pub fn to_container(&self) -> Option<&ContainerID> {
+    pub fn as_container(&self) -> Option<&ContainerID> {
+        match self {
+            LoroValue::Unresolved(c) => Some(c),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_map_mut(&mut self) -> Option<&mut FxHashMap<InternalString, LoroValue>> {
+        match self {
+            LoroValue::Map(m) => Some(m),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_list_mut(&mut self) -> Option<&mut Vec<LoroValue>> {
+        match self {
+            LoroValue::List(l) => Some(l),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_string_mut(&mut self) -> Option<&mut SmString> {
+        match self {
+            LoroValue::String(s) => Some(s),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_integer_mut(&mut self) -> Option<&mut i32> {
+        match self {
+            LoroValue::Integer(i) => Some(i),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_double_mut(&mut self) -> Option<&mut f64> {
+        match self {
+            LoroValue::Double(d) => Some(d),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_bool_mut(&mut self) -> Option<&mut bool> {
+        match self {
+            LoroValue::Bool(b) => Some(b),
+            _ => None,
+        }
+    }
+
+    #[inline]
+    pub fn as_container_mut(&mut self) -> Option<&mut ContainerID> {
         match self {
             LoroValue::Unresolved(c) => Some(c),
             _ => None,
diff --git a/crates/loro-core/src/version.rs b/crates/loro-core/src/version.rs
index 153ac9e8..7cd216f2 100644
--- a/crates/loro-core/src/version.rs
+++ b/crates/loro-core/src/version.rs
@@ -1,11 +1,225 @@
-use fxhash::FxHashMap;
+use std::{
+    cmp::Ordering,
+    collections::HashMap,
+    ops::{Deref, DerefMut},
+};
 
-use crate::{change::Lamport, ClientID};
+use fxhash::{FxBuildHasher, FxHashMap};
+use im::hashmap::HashMap as ImHashMap;
 
-pub type VersionVector = FxHashMap<ClientID, u32>;
+use crate::{
+    change::Lamport,
+    id::{Counter, ID},
+    span::IdSpan,
+    ClientID,
+};
+
+/// [VersionVector](https://en.wikipedia.org/wiki/Version_vector)
+///
+/// It's a map from [ClientID] to [Counter]. Its a right-open interval.
+/// i.e. a [VersionVector] of `{A: 1, B: 2}` means that A has 1 atomic op and B has 2 atomic ops,
+/// thus ID of `{client: A, counter: 1}` is out of the range.
+///
+/// In implementation, it's a immutable hash map with O(1) clone. Because
+/// - we want a cheap clone op on vv;
+/// - neighbor op's VersionVectors are very similar, most of the memory can be shared in
+/// immutable hashmap
+///
+/// see also [im].
+#[repr(transparent)]
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct VersionVector(ImHashMap<ClientID, Counter>);
+
+impl Deref for VersionVector {
+    type Target = ImHashMap<ClientID, Counter>;
+
+    fn deref(&self) -> &Self::Target {
+        &self.0
+    }
+}
+
+impl PartialOrd for VersionVector {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        let mut self_greater = true;
+        let mut other_greater = true;
+        let mut eq = true;
+        for (client_id, other_end) in other.iter() {
+            if let Some(self_end) = self.get(client_id) {
+                if self_end < other_end {
+                    self_greater = false;
+                    eq = false;
+                }
+                if self_end > other_end {
+                    other_greater = false;
+                    eq = false;
+                }
+            } else {
+                self_greater = false;
+                eq = false;
+            }
+        }
+
+        for (client_id, _) in self.iter() {
+            if other.contains_key(client_id) {
+                continue;
+            } else {
+                other_greater = false;
+                eq = false;
+            }
+        }
+
+        if eq {
+            Some(Ordering::Equal)
+        } else if self_greater {
+            Some(Ordering::Greater)
+        } else if other_greater {
+            Some(Ordering::Less)
+        } else {
+            None
+        }
+    }
+}
+
+impl DerefMut for VersionVector {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        &mut self.0
+    }
+}
+
+impl VersionVector {
+    #[inline]
+    pub fn new() -> Self {
+        Self(ImHashMap::new())
+    }
+
+    #[inline]
+    pub fn set_end(&mut self, id: ID) {
+        self.0.insert(id.client_id, id.counter + 1);
+    }
+
+    /// update the end counter of the given client, if the end is greater
+    /// return whether updated
+    #[inline]
+    pub fn try_update_end(&mut self, id: ID) -> bool {
+        if let Some(end) = self.0.get_mut(&id.client_id) {
+            if *end < id.counter + 1 {
+                *end = id.counter + 1;
+                true
+            } else {
+                false
+            }
+        } else {
+            self.0.insert(id.client_id, id.counter + 1);
+            true
+        }
+    }
+
+    pub fn get_missing_span(&self, target: &Self) -> Vec<IdSpan> {
+        let mut ans = vec![];
+        for (client_id, other_end) in target.iter() {
+            if let Some(my_end) = self.get(client_id) {
+                if my_end < other_end {
+                    ans.push(IdSpan::new(*client_id, *my_end, *other_end));
+                }
+            } else {
+                ans.push(IdSpan::new(*client_id, 0, *other_end));
+            }
+        }
+
+        ans
+    }
+
+    pub fn merge(&mut self, other: &Self) {
+        for (&client_id, &other_end) in other.iter() {
+            if let Some(my_end) = self.get_mut(&client_id) {
+                if *my_end < other_end {
+                    *my_end = other_end;
+                }
+            } else {
+                self.0.insert(client_id, other_end);
+            }
+        }
+    }
+
+    pub fn includes(&mut self, id: ID) -> bool {
+        if let Some(end) = self.get_mut(&id.client_id) {
+            if *end > id.counter {
+                return true;
+            }
+        }
+        false
+    }
+}
+
+impl Default for VersionVector {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl From<FxHashMap<ClientID, Counter>> for VersionVector {
+    fn from(map: FxHashMap<ClientID, Counter>) -> Self {
+        let mut im_map = ImHashMap::new();
+        for (client_id, counter) in map {
+            im_map.insert(client_id, counter);
+        }
+        Self(im_map)
+    }
+}
+
+impl From<Vec<ID>> for VersionVector {
+    fn from(vec: Vec<ID>) -> Self {
+        let mut vv = VersionVector::new();
+        for id in vec {
+            vv.set_end(id);
+        }
+
+        vv
+    }
+}
 
 #[derive(Debug, PartialEq, Eq, Clone, Copy, PartialOrd, Ord)]
 pub(crate) struct TotalOrderStamp {
     pub(crate) lamport: Lamport,
     pub(crate) client_id: ClientID,
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    mod cmp {
+        use super::*;
+        #[test]
+        fn test() {
+            let a: VersionVector = vec![ID::new(1, 1), ID::new(2, 2)].into();
+            let b: VersionVector = vec![ID::new(1, 1), ID::new(2, 2)].into();
+            assert_eq!(a.partial_cmp(&b), Some(Ordering::Equal));
+
+            let a: VersionVector = vec![ID::new(1, 2), ID::new(2, 1)].into();
+            let b: VersionVector = vec![ID::new(1, 1), ID::new(2, 2)].into();
+            assert_eq!(a.partial_cmp(&b), None);
+
+            let a: VersionVector = vec![ID::new(1, 2), ID::new(2, 3)].into();
+            let b: VersionVector = vec![ID::new(1, 1), ID::new(2, 2)].into();
+            assert_eq!(a.partial_cmp(&b), Some(Ordering::Greater));
+
+            let a: VersionVector = vec![ID::new(1, 0), ID::new(2, 2)].into();
+            let b: VersionVector = vec![ID::new(1, 1), ID::new(2, 2)].into();
+            assert_eq!(a.partial_cmp(&b), Some(Ordering::Less));
+        }
+    }
+
+    #[test]
+    fn im() {
+        let mut a = VersionVector::new();
+        a.set_end(ID::new(1, 1));
+        a.set_end(ID::new(2, 1));
+        let mut b = a.clone();
+        b.merge(&vec![ID::new(1, 2), ID::new(2, 2)].into());
+        assert!(a != b);
+        assert_eq!(a.get(&1), Some(&2));
+        assert_eq!(a.get(&2), Some(&2));
+        assert_eq!(b.get(&1), Some(&3));
+        assert_eq!(b.get(&2), Some(&3));
+    }
+}
diff --git a/crates/loro-framework/Cargo.toml b/crates/loro-framework/Cargo.toml
index 507ff84c..487889e3 100644
--- a/crates/loro-framework/Cargo.toml
+++ b/crates/loro-framework/Cargo.toml
@@ -11,3 +11,6 @@ loro-core = {path = "../loro-core"}
 ring = "0.16.20"
 rle = {path = "../rle"}
 sha2 = "0.10.2"
+
+[lib]
+doctest = false
diff --git a/crates/loro-framework/src/raw_store.rs b/crates/loro-framework/src/raw_store.rs
index ea01d912..7de5ebc5 100644
--- a/crates/loro-framework/src/raw_store.rs
+++ b/crates/loro-framework/src/raw_store.rs
@@ -1,5 +1,8 @@
 use fxhash::FxHashMap;
-use loro_core::{id::ClientID, version::VersionVector};
+use loro_core::{
+    id::{ClientID, Counter},
+    version::VersionVector,
+};
 use rle::RleVec;
 
 use crate::raw_change::{ChangeData, ChangeHash};
@@ -72,9 +75,9 @@ impl RawStore {
     }
 
     pub fn version_vector(&self) -> VersionVector {
-        let mut version_vector = FxHashMap::default();
+        let mut version_vector = VersionVector::new();
         for (client_id, changes) in &self.changes {
-            version_vector.insert(*client_id, changes.len() as u32);
+            version_vector.insert(*client_id, changes.len() as Counter);
         }
 
         version_vector
diff --git a/crates/rle/Cargo.toml b/crates/rle/Cargo.toml
index 19ed8d08..07b334c6 100644
--- a/crates/rle/Cargo.toml
+++ b/crates/rle/Cargo.toml
@@ -6,3 +6,4 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+num = "0.4.0"
diff --git a/crates/rle/src/lib.rs b/crates/rle/src/lib.rs
index 5af76106..f83e87b1 100644
--- a/crates/rle/src/lib.rs
+++ b/crates/rle/src/lib.rs
@@ -1,2 +1,24 @@
-mod rle;
-pub use crate::rle::{HasLength, Mergable, RleVec, SearchResult, Slice, SliceIterator, Sliceable};
+//! Run length encoding library.
+//!
+//! There are many mergeable types. By merging them together we can get a more compact representation of the data.
+//! For example, in many cases, `[0..5, 5..10]` can be merged into `0..10`.
+//!
+//! # RleVec
+//!
+//! RleVec<T> is a vector that can be compressed using run-length encoding.
+//!
+//! A T value may be merged with its neighbors. When we push new element, the new value
+//! may be merged with the last element in the array. Each value has a length, so there
+//! are two types of indexes:
+//! 1. (merged) It refers to the index of the merged element.
+//! 2. (atom) The index of substantial elements. It refers to the index of the atom element.
+//!
+//! By default, we use atom index in RleVec.
+//! - len() returns the number of atom elements in the array.
+//! - get(index) returns the atom element at the index.
+//! - slice(from, to) returns a slice of atom elements from the index from to the index to.
+//!
+mod rle_trait;
+mod rle_vec;
+pub use crate::rle_trait::{HasLength, Mergable, Rle, Slice, Sliceable};
+pub use crate::rle_vec::{RleVec, SearchResult, SliceIterator};
diff --git a/crates/rle/src/rle_trait.rs b/crates/rle/src/rle_trait.rs
new file mode 100644
index 00000000..d5ab3e81
--- /dev/null
+++ b/crates/rle/src/rle_trait.rs
@@ -0,0 +1,44 @@
+pub trait Mergable<Cfg = ()> {
+    fn is_mergable(&self, _other: &Self, _conf: &Cfg) -> bool
+    where
+        Self: Sized,
+    {
+        false
+    }
+
+    fn merge(&mut self, _other: &Self, _conf: &Cfg)
+    where
+        Self: Sized,
+    {
+        unreachable!()
+    }
+}
+
+pub trait Sliceable {
+    fn slice(&self, from: usize, to: usize) -> Self;
+}
+
+#[derive(Debug, Clone, Copy)]
+pub struct Slice<'a, T> {
+    pub value: &'a T,
+    pub start: usize,
+    pub end: usize,
+}
+
+impl<T: Sliceable> Slice<'_, T> {
+    pub fn into_inner(&self) -> T {
+        self.value.slice(self.start, self.end)
+    }
+}
+
+pub trait HasLength {
+    fn is_empty(&self) -> bool {
+        self.len() == 0
+    }
+
+    fn len(&self) -> usize;
+}
+
+pub trait Rle<Cfg = ()>: HasLength + Sliceable + Mergable<Cfg> {}
+
+impl<T: HasLength + Sliceable + Mergable<Cfg>, Cfg> Rle<Cfg> for T {}
diff --git a/crates/rle/src/rle.rs b/crates/rle/src/rle_vec.rs
similarity index 92%
rename from crates/rle/src/rle.rs
rename to crates/rle/src/rle_vec.rs
index a22717f2..f7e4e4a9 100644
--- a/crates/rle/src/rle.rs
+++ b/crates/rle/src/rle_vec.rs
@@ -1,4 +1,7 @@
-use std::ops::Range;
+use num::{cast, Integer, NumCast};
+use std::ops::{Range, Sub};
+
+use crate::{HasLength, Mergable, Rle, Slice, Sliceable};
 
 /// RleVec<T> is a vector that can be compressed using run-length encoding.
 ///
@@ -20,40 +23,6 @@ pub struct RleVec<T, Cfg = ()> {
     cfg: Cfg,
 }
 
-pub trait Mergable<Cfg = ()> {
-    fn is_mergable(&self, _other: &Self, _conf: &Cfg) -> bool
-    where
-        Self: Sized,
-    {
-        false
-    }
-
-    fn merge(&mut self, _other: &Self, _conf: &Cfg)
-    where
-        Self: Sized,
-    {
-        unreachable!()
-    }
-}
-
-pub trait Sliceable {
-    fn slice(&self, from: usize, to: usize) -> Self;
-}
-
-impl<T: Sliceable> Slice<'_, T> {
-    pub fn into_inner(&self) -> T {
-        self.value.slice(self.start, self.end)
-    }
-}
-
-pub trait HasLength {
-    fn is_empty(&self) -> bool {
-        self.len() == 0
-    }
-
-    fn len(&self) -> usize;
-}
-
 pub struct SearchResult<'a, T> {
     pub element: &'a T,
     pub merged_index: usize,
@@ -253,13 +222,6 @@ pub struct SliceIterator<'a, T> {
     end_offset: usize,
 }
 
-#[derive(Debug, Clone, Copy)]
-pub struct Slice<'a, T> {
-    pub value: &'a T,
-    pub start: usize,
-    pub end: usize,
-}
-
 impl<'a, T: HasLength> Iterator for SliceIterator<'a, T> {
     type Item = Slice<'a, T>;
 
@@ -316,6 +278,31 @@ impl<T> HasLength for RleVec<T> {
     }
 }
 
+impl<T: Integer + NumCast + Copy> Sliceable for Range<T> {
+    fn slice(&self, start: usize, end: usize) -> Self {
+        self.start + cast(start).unwrap()..self.start + cast(end).unwrap()
+    }
+}
+
+impl<T: PartialOrd<T> + Copy> Mergable for Range<T> {
+    fn is_mergable(&self, other: &Self, _: &()) -> bool {
+        other.start <= self.end && other.start >= self.start
+    }
+
+    fn merge(&mut self, other: &Self, _conf: &())
+    where
+        Self: Sized,
+    {
+        self.end = other.end;
+    }
+}
+
+impl<T: num::Integer + NumCast + Copy> HasLength for Range<T> {
+    fn len(&self) -> usize {
+        cast(self.end - self.start).unwrap()
+    }
+}
+
 #[cfg(test)]
 mod test {
     mod prime_value {
diff --git a/rust-toolchain b/rust-toolchain
index bf867e0a..2bf5ad04 100644
--- a/rust-toolchain
+++ b/rust-toolchain
@@ -1 +1 @@
-nightly
+stable