diff --git a/src/util/scoped_map.h b/src/util/scoped_map.h
index 5f4316d69..9dfa9bb40 100644
--- a/src/util/scoped_map.h
+++ b/src/util/scoped_map.h
@@ -33,7 +33,16 @@ public:
     explicit scoped_map(size_type bucket_count = LEAN_SCOPED_MAP_INITIAL_BUCKET_SIZE,
                         const Hash& hash = Hash(),
                         const KeyEqual& equal = KeyEqual()):
-        m_map(bucket_count, hash, equal) {}
+        m_map(bucket_count, hash, equal) {
+        // the return type of Hash()(k) should be convertible to size_t
+        static_assert(std::is_convertible<typename std::result_of<decltype(std::declval<Hash>())(Key const &)>::type,
+                                          std::size_t>::value,
+                      "The return type of hash function is not convertible to std::size_t");
+        // the return type of KeyEqual()(k1, k2) should be bool
+        static_assert(std::is_same<typename std::result_of<decltype(std::declval<KeyEqual>())(Key const &, Key const &)>::type,
+                                   bool>::value,
+                      "The return type of KeyEqual()(k1, k2) is not bool");
+    }
 
     void swap(scoped_map & other) {
         m_map.swap(other.m_map);
diff --git a/src/util/scoped_set.h b/src/util/scoped_set.h
index 22518bba6..9ec018e04 100644
--- a/src/util/scoped_set.h
+++ b/src/util/scoped_set.h
@@ -31,7 +31,16 @@ public:
     explicit scoped_set(size_type bucket_count = LEAN_SCOPED_SET_INITIAL_BUCKET_SIZE,
                         const Hash& hash = Hash(),
                         const KeyEqual& equal = KeyEqual()):
-        m_set(bucket_count, hash, equal) {}
+        m_set(bucket_count, hash, equal) {
+        // the return type of Hash()(k) should be convertible to size_t
+        static_assert(std::is_convertible<typename std::result_of<decltype(std::declval<Hash>())(Key const &)>::type,
+                                          std::size_t>::value,
+                      "The return type of hash function is not convertible to std::size_t");
+        // the return type of KeyEqual()(k1, k2) should be bool
+        static_assert(std::is_same<typename std::result_of<decltype(std::declval<KeyEqual>())(Key const &, Key const &)>::type,
+                                   bool>::value,
+                      "The return type of KeyEqual()(k1, k2) is not bool");
+    }
 
     /** \brief Return the number of scopes. */
     unsigned num_scopes() const {
diff --git a/src/util/splay_map.h b/src/util/splay_map.h
index cc6c1fdfe..c311dd6a3 100644
--- a/src/util/splay_map.h
+++ b/src/util/splay_map.h
@@ -22,8 +22,12 @@ class splay_map : public CMP {
     };
     splay_tree<entry, entry_cmp> m_map;
 public:
-    splay_map(CMP const & cmp = CMP()):m_map(entry_cmp(cmp)) {}
-
+    splay_map(CMP const & cmp = CMP()):m_map(entry_cmp(cmp)) {
+        // the return type of CMP()(k1, k2) should be int
+        static_assert(std::is_same<typename std::result_of<decltype(std::declval<CMP>())(K const &, K const &)>::type,
+                                   int>::value,
+                      "The return type of CMP()(k1, k2) is not int.");
+    }
     void swap(splay_map & m) { m_map.swap(m.m_map); }
     bool empty() const { return m_map.empty(); }
     void clear() { m_map.clear(); }
@@ -60,12 +64,16 @@ public:
 
     template<typename F, typename R>
     R fold(F f, R r) const {
+        static_assert(std::is_same<typename std::result_of<F(K const &, T const &, R const &)>::type, R>::value,
+                      "fold: return type of f(k : K, t : T, r : R) is not R");
         auto f_prime = [&](entry const & e, R r) -> R { return f(e.first, e.second, r); };
         return m_map.fold(f_prime, r);
     }
 
     template<typename F>
     void for_each(F f) const {
+        static_assert(std::is_same<typename std::result_of<F(K const &, T const &)>::type, void>::value,
+                      "for_each: return type of f is not void");
         auto f_prime = [&](entry const & e) { f(e.first, e.second); };
         return m_map.for_each(f_prime);
     }
@@ -94,10 +102,14 @@ splay_map<K, T, CMP> erase(splay_map<K, T, CMP> const & m, K const & k) {
 }
 template<typename K, typename T, typename CMP, typename F, typename R>
 R fold(splay_map<K, T, CMP> const & m, F f, R r) {
+    static_assert(std::is_same<typename std::result_of<F(K const &, T const &, R const &)>::type, R>::value,
+                  "fold: return type of f(k : K, t : T, r : R) is not R");
     return m.fold(f, r);
 }
 template<typename K, typename T, typename CMP, typename F>
 void for_each(splay_map<K, T, CMP> const & m, F f) {
+    static_assert(std::is_same<typename std::result_of<F(K const &, T const &)>::type, void>::value,
+                  "for_each: return type of f is not void");
     return m.for_each(f);
 }
 }
diff --git a/src/util/splay_tree.h b/src/util/splay_tree.h
index 7b5d5accb..8e2d96167 100644
--- a/src/util/splay_tree.h
+++ b/src/util/splay_tree.h
@@ -42,6 +42,10 @@ class splay_tree : public CMP {
         static void dec_ref(node * n) { if (n) n->dec_ref(); }
         explicit node(T const & v, node * left = nullptr, node * right = nullptr):
             m_left(left), m_right(right), m_value(v), m_rc(0) {
+            // the return type of CMP()(t1, 2) should be int
+            static_assert(std::is_same<typename std::result_of<decltype(std::declval<CMP>())(T const &, T const &)>::type,
+                                       int>::value,
+                          "The return type of CMP()(t1, t2) is not int.");
             inc_ref(m_left);
             inc_ref(m_right);
         }
@@ -289,6 +293,8 @@ class splay_tree : public CMP {
 
     template<typename F, typename R>
     static R fold(node const * n, F & f, R r) {
+        static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
+                      "fold: return type of f(t : T, r : R) is not R");
         if (n) {
             r = fold(n->m_left, f, r);
             r = f(n->m_value, r);
@@ -300,6 +306,8 @@ class splay_tree : public CMP {
 
     template<typename F>
     static void for_each(node const * n, F & f) {
+        static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
+                      "for_each: return type of f is not void");
         if (n) {
             for_each(n->m_left, f);
             f(n->m_value);
@@ -332,7 +340,7 @@ public:
     bool is_eqp(splay_tree const & t) const { return m_ptr == t.m_ptr; }
 
     /** \brief Return the size of the splay tree */
-    unsigned size() const { return fold([](T const &, unsigned a) { return a + 1; }, 0); }
+    unsigned size() const { return fold([](T const &, unsigned a) { return a + 1; }, 0u); }
 
     /** \brief Insert \c v in this splay tree. */
     void insert(T const & v) {
@@ -425,6 +433,8 @@ public:
     */
     template<typename F, typename R>
     R fold(F f, R r) const {
+        static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
+                      "fold: return type of f(t : T, r : R) is not R");
         return fold(m_ptr, f, r);
     }
 
@@ -433,6 +443,8 @@ public:
     */
     template<typename F>
     void for_each(F f) const {
+        static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
+                      "for_each: return type of f is not void");
         for_each(m_ptr, f);
     }
 };
@@ -442,10 +454,14 @@ template<typename T, typename CMP>
 splay_tree<T, CMP> erase(splay_tree<T, CMP> & t, T const & v) { splay_tree<T, CMP> r(t); r.erase(v); return r; }
 template<typename T, typename CMP, typename F, typename R>
 R fold(splay_tree<T, CMP> const & t, F f, R r) {
+    static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
+                  "fold: return type of f(t : T, r : R) is not R");
     return t.fold(f, r);
 }
 template<typename T, typename CMP, typename F>
 void for_each(splay_tree<T, CMP> const & t, F f) {
+    static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
+                  "for_each: return type of f is not void");
     return t.for_each(f);
 }
 }