diff --git a/include/iris/ngram/database.hpp b/include/iris/ngram/database.hpp
index 6ada138..34add63 100644
--- a/include/iris/ngram/database.hpp
+++ b/include/iris/ngram/database.hpp
@@ -74,8 +74,8 @@ class database
         store_.clear();
     }
 
-    template<class DocumentID = document_id>
-    bool search(this auto const& db, search_query<CharT> const& query, search_result<DocumentID>& search_res)
+    template<class DocumentID, class HashT, class EqualT>
+    bool search(this auto const& db, search_query<CharT> const& query, search_result<DocumentID, HashT, EqualT>& search_res)
     {
         search_res.clear();
         if (query.empty()) return false;
diff --git a/include/iris/ngram/keyed_database.hpp b/include/iris/ngram/keyed_database.hpp
index 8d0334b..37fb17c 100644
--- a/include/iris/ngram/keyed_database.hpp
+++ b/include/iris/ngram/keyed_database.hpp
@@ -8,8 +8,7 @@
 #include <iris/ngram/database.hpp>
 #include <iris/ngram/id.hpp>
 
-#include <iris/hash.hpp>
-
+#include <format>
 #include <unordered_map>
 #include <stdexcept>
 #include <memory>
@@ -25,7 +24,7 @@ class keyed_database : private database<CharT>
 public:
     using document_id_type = KeyT;
 
-    template<class KeyLikeT>
+    template<class KeyLikeT = KeyT>
         requires std::is_constructible_v<KeyT, KeyLikeT>
     void add_document(KeyLikeT&& key_like, std::basic_string_view<CharT> const doc_text)
     {
@@ -34,8 +33,10 @@ class keyed_database : private database<CharT>
         if (!inserted) {
             if constexpr (std::is_pointer_v<KeyT>) {
                 throwf<std::invalid_argument>("key `{}` already exists in keyed_database", static_cast<void const*>(it->first));
-            } else {
+            } else if constexpr (std::formattable<KeyT, char>) {
                 throwf<std::invalid_argument>("key `{}` already exists in keyed_database", it->first);
+            } else {
+                throwf<std::invalid_argument>("key `???` already exists in keyed_database");
             }
         }
         assert(doc_id_to_key_.size() == detail::to_index(doc_id));
@@ -48,7 +49,7 @@ class keyed_database : private database<CharT>
         base_type::update_document(this->get_document_id(key_like), doc_text);
     }
 
-    template<class KeyLikeT>
+    template<class KeyLikeT = KeyT>
         requires std::is_constructible_v<KeyT, KeyLikeT>
     void add_or_update_document(KeyLikeT&& key_like, std::basic_string_view<CharT> const doc_text)
     {
diff --git a/include/iris/ngram/search_result.hpp b/include/iris/ngram/search_result.hpp
index 7e39c5f..98fc639 100644
--- a/include/iris/ngram/search_result.hpp
+++ b/include/iris/ngram/search_result.hpp
@@ -59,11 +59,13 @@ struct [[nodiscard]] search_word_match
     std::vector<interval<int>> spans_;
 };
 
-template<class DocumentID = document_id>
+template<class DocumentID = document_id, class HashT = std::hash<DocumentID>, class EqualT = std::equal_to<>>
 struct [[nodiscard]] search_result
 {
     using document_id_type = DocumentID;
-    using map_type = std::unordered_map<DocumentID, std::vector<search_word_match>>;
+    using hash_type = HashT;
+    using equal_type = EqualT;
+    using map_type = std::unordered_map<DocumentID, std::vector<search_word_match>, HashT, EqualT>;
 
     search_result() = default;