diff --git a/src/kernel/type_checker.cpp b/src/kernel/type_checker.cpp
index 0c481b51f9..74368d2e7b 100644
--- a/src/kernel/type_checker.cpp
+++ b/src/kernel/type_checker.cpp
@@ -487,6 +487,20 @@ struct type_checker::imp {
         return r;
     }
     expr whnf(expr const & t) { return m_conv->whnf(t, m_conv_ctx); }
+    void push() {
+        lean_assert(!m_cache_cs);
+        m_infer_type_cache[0].push();
+        m_infer_type_cache[1].push();
+    }
+    void pop() {
+        lean_assert(!m_cache_cs);
+        m_infer_type_cache[0].pop();
+        m_infer_type_cache[1].pop();
+    }
+    unsigned num_scopes() const {
+        lean_assert(m_infer_type_cache[0].num_scopes() == m_infer_type_cache[1].num_scopes());
+        return m_infer_type_cache[0].num_scopes();
+    }
 };
 
 static add_cnstr_fn g_no_constraint_fn = mk_no_contranint_fn();
@@ -512,6 +526,9 @@ bool type_checker::is_prop(expr const & t) { return m_ptr->is_prop(t); }
 expr type_checker::whnf(expr const & t) { return m_ptr->whnf(t); }
 expr type_checker::ensure_pi(expr const & t, expr const & s) { return m_ptr->ensure_pi(t, s); }
 expr type_checker::ensure_sort(expr const & t, expr const & s) { return m_ptr->ensure_sort(t, s); }
+void type_checker::push() { m_ptr->push(); }
+void type_checker::pop() { m_ptr->pop(); }
+unsigned type_checker::num_scopes() const { return m_ptr->num_scopes(); }
 
 static void check_no_metavar(environment const & env, expr const & e) {
     if (has_metavar(e))
diff --git a/src/kernel/type_checker.h b/src/kernel/type_checker.h
index 54f1f0d9b2..fd8f98d158 100644
--- a/src/kernel/type_checker.h
+++ b/src/kernel/type_checker.h
@@ -100,6 +100,13 @@ public:
     /** \brief Mare sure type of \c e is a sort, and return it. Throw an exception otherwise. */
     expr ensure_type(expr const & e) { return ensure_sort(infer(e), e); }
 
+    /** \brief Create a backtracking point for cache and generated constraints. */
+    void push();
+    /** \brief Restore backtracking point. */
+    void pop();
+    /** \brief Return the number of backtracking points. */
+    unsigned num_scopes() const;
+
     void swap(type_checker & tc) { std::swap(m_ptr, tc.m_ptr); }
 };
 
diff --git a/src/library/kernel_bindings.cpp b/src/library/kernel_bindings.cpp
index 7f7f413f19..fb73e691c4 100644
--- a/src/library/kernel_bindings.cpp
+++ b/src/library/kernel_bindings.cpp
@@ -1830,7 +1830,7 @@ static void get_type_checker_args(lua_State * L, int idx, optional<module_idx> &
     extra_opaque = get_name_set_named_param(L, idx, "extra_opaque", name_set());
 }
 
-int mk_type_checker(lua_State * L) {
+static int mk_type_checker(lua_State * L) {
     int nargs = lua_gettop(L);
     if (nargs == 1) {
         return push_type_checker_ref(L, std::make_shared<type_checker>(to_environment(L, 1)));
@@ -1857,29 +1857,37 @@ int mk_type_checker(lua_State * L) {
         }
     }
 }
-int type_checker_whnf(lua_State * L) { return push_expr(L, to_type_checker_ref(L, 1)->whnf(to_expr(L, 2))); }
-int type_checker_ensure_pi(lua_State * L) {
+static int type_checker_whnf(lua_State * L) { return push_expr(L, to_type_checker_ref(L, 1)->whnf(to_expr(L, 2))); }
+static int type_checker_ensure_pi(lua_State * L) {
     if (lua_gettop(L) == 2)
         return push_expr(L, to_type_checker_ref(L, 1)->ensure_pi(to_expr(L, 2)));
     else
         return push_expr(L, to_type_checker_ref(L, 1)->ensure_pi(to_expr(L, 2), to_expr(L, 3)));
 }
-int type_checker_ensure_sort(lua_State * L) {
+static int type_checker_ensure_sort(lua_State * L) {
     if (lua_gettop(L) == 2)
         return push_expr(L, to_type_checker_ref(L, 1)->ensure_sort(to_expr(L, 2)));
     else
         return push_expr(L, to_type_checker_ref(L, 1)->ensure_sort(to_expr(L, 2), to_expr(L, 3)));
 }
-int type_checker_check(lua_State * L) {
+static int type_checker_check(lua_State * L) {
     int nargs = lua_gettop(L);
     if (nargs <= 2)
         return push_expr(L, to_type_checker_ref(L, 1)->check(to_expr(L, 2), level_param_names()));
     else
         return push_expr(L, to_type_checker_ref(L, 1)->check(to_expr(L, 2), to_level_param_names(L, 3)));
 }
-int type_checker_infer(lua_State * L) { return push_expr(L, to_type_checker_ref(L, 1)->infer(to_expr(L, 2))); }
-int type_checker_is_def_eq(lua_State * L) { return push_boolean(L, to_type_checker_ref(L, 1)->is_def_eq(to_expr(L, 2), to_expr(L, 3))); }
-int type_checker_is_prop(lua_State * L) { return push_boolean(L, to_type_checker_ref(L, 1)->is_prop(to_expr(L, 2))); }
+static int type_checker_infer(lua_State * L) { return push_expr(L, to_type_checker_ref(L, 1)->infer(to_expr(L, 2))); }
+static int type_checker_is_def_eq(lua_State * L) { return push_boolean(L, to_type_checker_ref(L, 1)->is_def_eq(to_expr(L, 2), to_expr(L, 3))); }
+static int type_checker_is_prop(lua_State * L) { return push_boolean(L, to_type_checker_ref(L, 1)->is_prop(to_expr(L, 2))); }
+static int type_checker_push(lua_State * L) { to_type_checker_ref(L, 1)->push(); return 0; }
+static int type_checker_pop(lua_State * L) {
+    if (to_type_checker_ref(L, 1)->num_scopes() == 0)
+        throw exception("invalid pop method, type_checker does not have backtracking points");
+    to_type_checker_ref(L, 1)->pop();
+    return 0;
+}
+static int type_checker_num_scopes(lua_State * L) { return push_integer(L, to_type_checker_ref(L, 1)->num_scopes()); }
 
 static const struct luaL_Reg type_checker_ref_m[] = {
     {"__gc",        type_checker_ref_gc},
@@ -1890,6 +1898,9 @@ static const struct luaL_Reg type_checker_ref_m[] = {
     {"infer",       safe_function<type_checker_infer>},
     {"is_def_eq",   safe_function<type_checker_is_def_eq>},
     {"is_prop",     safe_function<type_checker_is_prop>},
+    {"push",        safe_function<type_checker_push>},
+    {"pop",         safe_function<type_checker_pop>},
+    {"num_scopes",  safe_function<type_checker_num_scopes>},
     {0, 0}
 };
 
diff --git a/tests/lua/tc8.lua b/tests/lua/tc8.lua
new file mode 100644
index 0000000000..f5f9fe76de
--- /dev/null
+++ b/tests/lua/tc8.lua
@@ -0,0 +1,22 @@
+local env = environment()
+local N   = Const("N")
+env = add_decl(env, mk_var_decl("N", Type))
+env = add_decl(env, mk_var_decl("f", mk_arrow(N, N)))
+env = add_decl(env, mk_var_decl("a", N))
+local f = Const("f")
+local a = Const("a")
+local m1   = mk_metavar("m1", mk_metavar("m2", mk_sort(mk_meta_univ("l"))))
+local cs   = {}
+local ngen = name_generator("tst")
+local tc   = type_checker(env, ngen, function (c) print(c); cs[#cs+1] = c end)
+assert(tc:num_scopes() == 0)
+tc:push()
+assert(tc:num_scopes() == 1)
+print(tc:check(f(m1)))
+assert(#cs == 1)
+print(tc:check(f(f(m1))))
+assert(#cs == 1) -- New constraint is not generated
+tc:pop() -- forget that we checked f(m1)
+print(tc:check(f(m1)))
+assert(#cs == 2) -- constraint is generated again
+check_error(function() tc:pop() end)