diff --git a/src/kernel/expr.cpp b/src/kernel/expr.cpp
index 0645516e5..4a32662f2 100644
--- a/src/kernel/expr.cpp
+++ b/src/kernel/expr.cpp
@@ -137,6 +137,10 @@ void expr_app::dealloc(buffer<expr_cell*> & todelete) {
 
 static unsigned dec(unsigned k) { return k == 0 ? 0 : k - 1; }
 
+bool operator==(expr_binder_info const & i1, expr_binder_info const & i2) {
+    return i1.is_implicit() == i2.is_implicit() && i1.is_cast() == i2.is_cast() && i1.is_contextual() == i2.is_contextual();
+}
+
 // Expr binders (Lambda, Pi)
 expr_binder::expr_binder(expr_kind k, name const & n, expr const & t, expr const & b, expr_binder_info const & i):
     expr_composite(k, ::lean::hash(t.hash(), b.hash()),
@@ -390,6 +394,7 @@ unsigned get_free_var_range(expr const & e) {
 }
 
 bool operator==(expr const & a, expr const & b) { return expr_eq_fn()(a, b); }
+bool is_bi_equal(expr const & a, expr const & b) { return expr_eq_fn(true)(a, b); }
 
 static expr copy_tag(expr const & e, expr && new_e) {
     tag t = e.get_tag();
diff --git a/src/kernel/expr.h b/src/kernel/expr.h
index 7de639ee1..f55c3daa7 100644
--- a/src/kernel/expr.h
+++ b/src/kernel/expr.h
@@ -150,8 +150,11 @@ public:
 
 // =======================================
 // Structural equality
-       bool operator==(expr const & a, expr const & b);
+/** \brief Binder information is ignored in the following predicate */
+bool operator==(expr const & a, expr const & b);
 inline bool operator!=(expr const & a, expr const & b) { return !operator==(a, b); }
+/** \brief Similar to ==, but it also compares binder information */
+bool is_bi_equal(expr const & a, expr const & b);
 // =======================================
 
 SPECIALIZE_OPTIONAL_FOR_SMART_PTR(expr)
@@ -232,6 +235,9 @@ public:
     bool is_contextual() const { return m_contextual; }
 };
 
+bool operator==(expr_binder_info const & i1, expr_binder_info const & i2);
+inline bool operator!=(expr_binder_info const & i1, expr_binder_info const & i2) { return !(i1 == i2); }
+
 /** \brief Super class for lambda and pi */
 class expr_binder : public expr_composite {
     name             m_name;
diff --git a/src/kernel/expr_eq_fn.cpp b/src/kernel/expr_eq_fn.cpp
index f5a81d303..5f4828024 100644
--- a/src/kernel/expr_eq_fn.cpp
+++ b/src/kernel/expr_eq_fn.cpp
@@ -39,7 +39,8 @@ bool expr_eq_fn::apply(expr const & a, expr const & b) {
     case expr_kind::Lambda: case expr_kind::Pi:
         return
             apply(binder_domain(a), binder_domain(b)) &&
-            apply(binder_body(a), binder_body(b));
+            apply(binder_body(a), binder_body(b)) &&
+            (!m_compare_binder_info || binder_info(a) == binder_info(b));
     case expr_kind::Sort:
         return sort_level(a) == sort_level(b);
     case expr_kind::Macro:
diff --git a/src/kernel/expr_eq_fn.h b/src/kernel/expr_eq_fn.h
index 1ecb1e828..e37eefcf4 100644
--- a/src/kernel/expr_eq_fn.h
+++ b/src/kernel/expr_eq_fn.h
@@ -15,9 +15,12 @@ namespace lean {
    \brief Functional object for comparing expressions.
 */
 class expr_eq_fn {
+    bool m_compare_binder_info;
     std::unique_ptr<expr_cell_pair_set> m_eq_visited;
     bool apply(expr const & a, expr const & b);
 public:
+    /** \brief If \c is true, then functional object will also compare binder information attached to lambda and Pi expressions */
+    expr_eq_fn(bool c = false):m_compare_binder_info(c) {}
     bool operator()(expr const & a, expr const & b) { return apply(a, b); }
     void clear() { m_eq_visited.reset(); }
 };
diff --git a/src/kernel/expr_maps.h b/src/kernel/expr_maps.h
index 2050eed32..74b04b14e 100644
--- a/src/kernel/expr_maps.h
+++ b/src/kernel/expr_maps.h
@@ -26,4 +26,8 @@ using expr_cell_offset_map = typename std::unordered_map<expr_cell_offset, T, ex
 // Maps based on structural equality. That is, two keys are equal iff they are structurally equal
 template<typename T>
 using expr_struct_map = typename std::unordered_map<expr, T, expr_hash, std::equal_to<expr>>;
+// The following map also takes into account binder information
+struct is_bi_equal_proc { bool operator()(expr const & e1, expr const & e2) const { return is_bi_equal(e1, e2); } };
+template<typename T>
+using expr_bi_struct_map = typename std::unordered_map<expr, T, expr_hash, is_bi_equal_proc>;
 };
diff --git a/src/kernel/type_checker.cpp b/src/kernel/type_checker.cpp
index 3c37faa07..beb680f79 100644
--- a/src/kernel/type_checker.cpp
+++ b/src/kernel/type_checker.cpp
@@ -60,7 +60,11 @@ struct type_checker::imp {
     name_generator             m_gen;
     constraint_handler &       m_chandler;
     std::unique_ptr<converter> m_conv;
-    expr_struct_map<expr>      m_infer_type_cache;
+    // In the type checker cache, we must take into account binder information.
+    // Examples:
+    // The type of (lambda x : A, t)   is (Pi x : A, typeof(t))
+    // The type of (lambda {x : A}, t) is (Pi {x : A}, typeof(t))
+    expr_bi_struct_map<expr>   m_infer_type_cache;
     converter_context          m_conv_ctx;
     type_checker_context       m_tc_ctx;
     bool                       m_memoize;
diff --git a/tests/lua/tc3.lua b/tests/lua/tc3.lua
new file mode 100644
index 000000000..d9c8ba8c2
--- /dev/null
+++ b/tests/lua/tc3.lua
@@ -0,0 +1,14 @@
+local env = empty_environment()
+local t1  = mk_lambda("A", Type, mk_lambda("a", Var(0), Var(0)), binder_info(true))
+local t2  = mk_lambda("A", Type, mk_lambda("a", Var(0), Var(0)))
+print(t1)
+print(t2)
+local tc  = type_checker(env)
+local T1  = mk_pi("A", Type, mk_arrow(Var(0), Var(1)), binder_info(true))
+local T2  = mk_pi("A", Type, mk_arrow(Var(0), Var(1)))
+print(T1)
+print(T2)
+print(tc:check(t1))
+print(tc:check(t2))
+assert(tc:check(t1):binder_info():is_implicit())
+assert(not tc:check(t2):binder_info():is_implicit())