diff --git a/apps/emqx_replay/src/emqx_replay_local_store.erl b/apps/emqx_replay/src/emqx_replay_local_store.erl
index 0138ffed5..35a31e65c 100644
--- a/apps/emqx_replay/src/emqx_replay_local_store.erl
+++ b/apps/emqx_replay/src/emqx_replay_local_store.erl
@@ -98,7 +98,7 @@ store(Zone, GUID, Time, Topic, Msg) ->
     #{module := Mod, data := Data} = meta_lookup_gen(Zone, Time),
     Mod:store(Data, GUID, Time, Topic, Msg).
 
--spec make_iterator(emqx_types:zone(), emqx_topic:words(), emqx_replay_message_storage:time()) ->
+-spec make_iterator(emqx_types:zone(), emqx_topic:words(), emqx_replay:time()) ->
     {ok, _TODO} | {error, _TODO}.
 make_iterator(Zone, TopicFilter, StartTime) ->
     %% TODO: this is not supposed to work like this. Just a mock-up
diff --git a/apps/emqx_replay/src/emqx_replay_message_storage.erl b/apps/emqx_replay/src/emqx_replay_message_storage.erl
index f2a6afaa6..fb96863d1 100644
--- a/apps/emqx_replay/src/emqx_replay_message_storage.erl
+++ b/apps/emqx_replay/src/emqx_replay_message_storage.erl
@@ -140,11 +140,8 @@
 %% Type declarations
 %%================================================================================
 
-%% parsed
--type topic() :: list(binary()).
-
-%% TODO granularity?
--type time() :: integer().
+-type topic() :: emqx_replay:topic().
+-type time() :: emqx_replay:time().
 
 %% Number of bits
 -type bits() :: non_neg_integer().
@@ -292,20 +289,19 @@ store(DB = #db{handle = DBHandle, cf = CFHandle}, MessageID, PublishedAt, Topic,
     Value = make_message_value(Topic, MessagePayload),
     rocksdb:put(DBHandle, CFHandle, Key, Value, DB#db.write_options).
 
--spec make_iterator(db(), emqx_topic:words(), time() | earliest) ->
+-spec make_iterator(db(), emqx_topic:words(), time()) ->
     {ok, iterator()} | {error, _TODO}.
 make_iterator(DB, TopicFilter, StartTime) ->
     Options = emqx_replay_conf:zone_iteration_options(DB#db.zone),
     make_iterator(DB, TopicFilter, StartTime, Options).
 
--spec make_iterator(db(), emqx_topic:words(), time() | earliest, iteration_options()) ->
+-spec make_iterator(db(), emqx_topic:words(), time(), iteration_options()) ->
     % {error, invalid_start_time}? might just start from the beginning of time
     % and call it a day: client violated the contract anyway.
     {ok, iterator()} | {error, _TODO}.
 make_iterator(DB = #db{handle = DBHandle, cf = CFHandle}, TopicFilter, StartTime, Options) ->
     case rocksdb:iterator(DBHandle, CFHandle, DB#db.read_options) of
         {ok, ITHandle} ->
-            % TODO earliest
             Filter = make_keyspace_filter(TopicFilter, StartTime, DB#db.keymapper),
             InitialSeek = combine(compute_initial_seek(Filter), <<>>, DB#db.keymapper),
             RefreshCounter = make_refresh_counter(maps:get(iterator_refresh, Options, undefined)),