diff --git a/src/kernel/expr.h b/src/kernel/expr.h
index 44fc50ede..63b135d97 100644
--- a/src/kernel/expr.h
+++ b/src/kernel/expr.h
@@ -583,6 +583,9 @@ template<typename F> expr update_eq(expr const & e, F f) {
         return e;
 }
 template<typename F> expr update_metavar(expr const & e, unsigned i, F f) {
+    static_assert(std::is_same<typename std::result_of<F(meta_entry const &)>::type,
+                               meta_entry>::value,
+                  "update_metavar: return type of f(meta_entry) is not meta_entry");
     buffer<meta_entry> new_entries;
     bool modified = (i != metavar_idx(e));
     for (meta_entry const & me : metavar_ctx(e)) {
@@ -603,6 +606,9 @@ template<typename F> expr update_metavar(expr const & e, unsigned i, F f) {
         return e;
 }
 template<typename F> expr update_metavar(expr const & e, F f) {
+    static_assert(std::is_same<typename std::result_of<F(meta_entry const &)>::type,
+                               meta_entry>::value,
+                  "update_metavar: return type of f(meta_entry) is not meta_entry");
     return update_metavar(e, metavar_idx(e), f);
 }
 // =======================================
diff --git a/src/kernel/expr_eq.h b/src/kernel/expr_eq.h
index 5a02036f6..9c9244fcb 100644
--- a/src/kernel/expr_eq.h
+++ b/src/kernel/expr_eq.h
@@ -71,7 +71,12 @@ class expr_eq_fn {
         lean_unreachable();
     }
 public:
-    expr_eq_fn(N const & norm = N()):m_norm(norm) {}
+    expr_eq_fn(N const & norm = N()):m_norm(norm) {
+        // the return type of N()(e) should be expr const &
+        static_assert(std::is_same<typename std::result_of<decltype(std::declval<N>())(expr const &)>::type,
+                      expr const &>::value,
+                      "The return type of CMP()(k1, k2) is not int.");
+    }
     bool operator()(expr const & a, expr const & b) {
         return apply(a, b);
     }
diff --git a/src/kernel/replace.h b/src/kernel/replace.h
index 1b866a126..e972e56a1 100644
--- a/src/kernel/replace.h
+++ b/src/kernel/replace.h
@@ -36,6 +36,11 @@ template<typename F, typename P = default_replace_postprocessor>
 class replace_fn {
     static_assert(std::is_same<typename std::result_of<F(expr const &, unsigned)>::type, expr>::value,
                   "replace_fn: return type of F is not expr");
+    // the return type of P()(e1, e2) should be void
+    static_assert(std::is_same<typename std::result_of<decltype(std::declval<P>())(expr const &, expr const &)>::type,
+                  void>::value,
+                  "The return type of P()(e1, e2) is not void");
+
     expr_cell_offset_map<expr> m_cache;
     F                          m_f;
     P                          m_post;