diff --git a/src/kernel/expr.cpp b/src/kernel/expr.cpp
index 9808d55aa..e30f6f550 100644
--- a/src/kernel/expr.cpp
+++ b/src/kernel/expr.cpp
@@ -37,9 +37,11 @@ bool has_meta(levels const & ls) {
     return false;
 }
 
-expr_cell::expr_cell(expr_kind k, unsigned h, bool has_mv):
+expr_cell::expr_cell(expr_kind k, unsigned h, bool has_mv, bool has_local):
     m_kind(static_cast<unsigned>(k)),
-    m_flags(has_mv ? 4 : 0),
+    m_flags(0),
+    m_has_mv(has_mv),
+    m_has_local(has_local),
     m_hash(h),
     m_rc(0) {
     // m_hash_alloc does not need to be a unique identifier.
@@ -63,8 +65,8 @@ void expr_cell::dec_ref(expr & e, buffer<expr_cell*> & todelete) {
 }
 
 optional<bool> expr_cell::is_arrow() const {
-    // it is stored in bits 3-4
-    unsigned r = (m_flags & (8+16)) >> 3;
+    // it is stored in bits 2-3
+    unsigned r = (m_flags & (4+8)) >> 2;
     if (r == 0) {
         return optional<bool>();
     } else if (r == 1) {
@@ -76,25 +78,25 @@ optional<bool> expr_cell::is_arrow() const {
 }
 
 void expr_cell::set_is_arrow(bool flag) {
-    unsigned mask = flag ? 8 : 16;
+    unsigned mask = flag ? 4 : 8;
     m_flags |= mask;
     lean_assert(is_arrow() && *is_arrow() == flag);
 }
 
 // Expr variables
 expr_var::expr_var(unsigned idx):
-    expr_cell(expr_kind::Var, idx, false),
+    expr_cell(expr_kind::Var, idx, false, false),
     m_vidx(idx) {}
 
 // Expr constants
 expr_const::expr_const(name const & n, levels const & ls):
-    expr_cell(expr_kind::Constant, ::lean::hash(n.hash(), hash_levels(ls)), has_meta(ls)),
+    expr_cell(expr_kind::Constant, ::lean::hash(n.hash(), hash_levels(ls)), has_meta(ls), false),
     m_name(n),
     m_levels(ls) {}
 
 // Expr metavariables and local variables
 expr_mlocal::expr_mlocal(bool is_meta, name const & n, expr const & t):
-    expr_cell(is_meta ? expr_kind::Meta : expr_kind::Local, n.hash(), is_meta || t.has_metavar()),
+    expr_cell(is_meta ? expr_kind::Meta : expr_kind::Local, n.hash(), is_meta || t.has_metavar(), !is_meta || t.has_local()),
     m_name(n),
     m_type(t) {}
 void expr_mlocal::dealloc(buffer<expr_cell*> & todelete) {
@@ -103,13 +105,15 @@ void expr_mlocal::dealloc(buffer<expr_cell*> & todelete) {
 }
 
 // Composite expressions
-expr_composite::expr_composite(expr_kind k, unsigned h, bool has_mv, unsigned d):
-    expr_cell(k, h, has_mv),
+expr_composite::expr_composite(expr_kind k, unsigned h, bool has_mv, bool has_local, unsigned d):
+    expr_cell(k, h, has_mv, has_local),
     m_depth(d) {}
 
 // Expr dependent pairs
 expr_dep_pair::expr_dep_pair(expr const & f, expr const & s, expr const & t):
-    expr_composite(expr_kind::Pair, ::lean::hash(f.hash(), s.hash()), f.has_metavar() || s.has_metavar() || t.has_metavar(),
+    expr_composite(expr_kind::Pair, ::lean::hash(f.hash(), s.hash()),
+                   f.has_metavar() || s.has_metavar() || t.has_metavar(),
+                   f.has_local() || s.has_local() || t.has_local(),
                    std::max(get_depth(f), get_depth(s))+1),
     m_first(f), m_second(s), m_type(t) {
 }
@@ -122,7 +126,7 @@ void expr_dep_pair::dealloc(buffer<expr_cell*> & todelete) {
 
 // Expr pair projection
 expr_proj::expr_proj(bool f, expr const & e):
-    expr_composite(f ? expr_kind::Fst : expr_kind::Snd, ::lean::hash(17, e.hash()), e.has_metavar(), get_depth(e)+1),
+    expr_composite(f ? expr_kind::Fst : expr_kind::Snd, ::lean::hash(17, e.hash()), e.has_metavar(), e.has_local(), get_depth(e)+1),
     m_expr(e) {}
 void expr_proj::dealloc(buffer<expr_cell*> & todelete) {
     dec_ref(m_expr, todelete);
@@ -131,7 +135,9 @@ void expr_proj::dealloc(buffer<expr_cell*> & todelete) {
 
 // Expr applications
 expr_app::expr_app(expr const & fn, expr const & arg):
-    expr_composite(expr_kind::App, ::lean::hash(fn.hash(), arg.hash()), fn.has_metavar() || arg.has_metavar(),
+    expr_composite(expr_kind::App, ::lean::hash(fn.hash(), arg.hash()),
+                   fn.has_metavar() || arg.has_metavar(),
+                   fn.has_local()   || arg.has_local(),
                    std::max(get_depth(fn), get_depth(arg)) + 1),
     m_fn(fn), m_arg(arg) {}
 void expr_app::dealloc(buffer<expr_cell*> & todelete) {
@@ -142,7 +148,9 @@ void expr_app::dealloc(buffer<expr_cell*> & todelete) {
 
 // Expr binders (Lambda, Pi and Sigma)
 expr_binder::expr_binder(expr_kind k, name const & n, expr const & t, expr const & b):
-    expr_composite(k, ::lean::hash(t.hash(), b.hash()), t.has_metavar() || b.has_metavar(),
+    expr_composite(k, ::lean::hash(t.hash(), b.hash()),
+                   t.has_metavar() || b.has_metavar(),
+                   t.has_local() || b.has_local(),
                    std::max(get_depth(t), get_depth(b)) + 1),
     m_name(n),
     m_domain(t),
@@ -157,14 +165,16 @@ void expr_binder::dealloc(buffer<expr_cell*> & todelete) {
 
 // Expr Sort
 expr_sort::expr_sort(level const & l):
-    expr_cell(expr_kind::Sort, ::lean::hash(l), has_meta(l)),
+    expr_cell(expr_kind::Sort, ::lean::hash(l), has_meta(l), false),
     m_level(l) {
 }
 expr_sort::~expr_sort() {}
 
 // Expr Let
 expr_let::expr_let(name const & n, expr const & t, expr const & v, expr const & b):
-    expr_composite(expr_kind::Let, ::lean::hash(v.hash(), b.hash()), t.has_metavar() || v.has_metavar() || b.has_metavar(),
+    expr_composite(expr_kind::Let, ::lean::hash(v.hash(), b.hash()),
+                   t.has_metavar() || v.has_metavar() || b.has_metavar(),
+                   t.has_local() || v.has_local() || b.has_local(),
                    std::max({get_depth(t), get_depth(v), get_depth(b)}) + 1),
     m_name(n),
     m_type(t),
@@ -215,7 +225,7 @@ static expr read_macro(deserializer & d) {
 }
 
 expr_macro::expr_macro(macro * m):
-    expr_cell(expr_kind::Macro, m->hash(), false),
+    expr_cell(expr_kind::Macro, m->hash(), false, false),
     m_macro(m) {
     m_macro->inc_ref();
 }
diff --git a/src/kernel/expr.h b/src/kernel/expr.h
index c722b2f11..af87ddc4d 100644
--- a/src/kernel/expr.h
+++ b/src/kernel/expr.h
@@ -51,11 +51,13 @@ protected:
     // The bits of the following field mean:
     //    0    - term is maximally shared
     //    1    - term is closed
-    //    2    - term contains metavariables
-    //    3-4  - term is an arrow (0 - not initialized, 1 - is arrow, 2 - is not arrow)
-    atomic_ushort      m_flags;
-    unsigned m_hash;       // hash based on the structure of the expression (this is a good hash for structural equality)
-    unsigned m_hash_alloc; // hash based on 'time' of allocation (this is a good hash for pointer-based equality)
+    //    2-3  - term is an arrow (0 - not initialized, 1 - is arrow, 2 - is not arrow)
+    // Remark: we use atomic_uchar because these flags are computed lazily (i.e., after the expression is created)
+    atomic_uchar       m_flags;
+    unsigned           m_has_mv:1;    // term contains metavariables
+    unsigned           m_has_local:1; // term contains local constants
+    unsigned           m_hash;        // hash based on the structure of the expression (this is a good hash for structural equality)
+    unsigned           m_hash_alloc;  // hash based on 'time' of allocation (this is a good hash for pointer-based equality)
     MK_LEAN_RC(); // Declare m_rc counter
     void dealloc();
 
@@ -73,11 +75,12 @@ protected:
     friend class has_free_var_fn;
     static void dec_ref(expr & c, buffer<expr_cell*> & todelete);
 public:
-    expr_cell(expr_kind k, unsigned h, bool has_mv);
+    expr_cell(expr_kind k, unsigned h, bool has_mv, bool has_local);
     expr_kind kind() const { return static_cast<expr_kind>(m_kind); }
     unsigned  hash() const { return m_hash; }
     unsigned  hash_alloc() const { return m_hash_alloc; }
-    bool has_metavar() const { return (m_flags & 4) != 0; }
+    bool has_metavar() const { return m_has_mv; }
+    bool has_local() const { return m_has_local; }
 };
 
 class macro;
@@ -115,6 +118,7 @@ public:
     unsigned  hash() const { return m_ptr ? m_ptr->hash() : 23; }
     unsigned  hash_alloc() const { return m_ptr ? m_ptr->hash_alloc() : 23; }
     bool has_metavar() const { return m_ptr->has_metavar(); }
+    bool has_local() const { return m_ptr->has_local(); }
 
     expr_cell * raw() const { return m_ptr; }
 
@@ -194,7 +198,7 @@ class expr_composite : public expr_cell {
     unsigned m_depth;
     friend unsigned get_depth(expr const & e);
 public:
-    expr_composite(expr_kind k, unsigned h, bool has_mv, unsigned d);
+    expr_composite(expr_kind k, unsigned h, bool has_mv, bool has_local, unsigned d);
 };
 
 /** \brief Applications */
@@ -510,6 +514,7 @@ inline expr const &   mlocal_type(expr const & e)          { return to_mlocal(e)
 
 inline bool is_constant(expr const & e, name const & n) { return is_constant(e) && const_name(e) == n; }
 inline bool has_metavar(expr const & e) { return e.has_metavar(); }
+inline bool has_local(expr const & e) { return e.has_local(); }
 unsigned get_depth(expr const & e);
 // =======================================
 
diff --git a/src/tests/kernel/expr.cpp b/src/tests/kernel/expr.cpp
index edeba03b0..1a6bc6c1b 100644
--- a/src/tests/kernel/expr.cpp
+++ b/src/tests/kernel/expr.cpp
@@ -303,6 +303,15 @@ static void tst15() {
     lean_assert(has_metavar(f(a, a, m)));
     lean_assert(has_metavar(f(a, m, a, a)));
     lean_assert(!has_metavar(f(a, a, a, a)));
+    lean_assert(!has_metavar(mk_fst(a)));
+    lean_assert(!has_metavar(mk_snd(a)));
+    lean_assert(has_metavar(mk_fst(m)));
+    lean_assert(has_metavar(mk_snd(m)));
+    lean_assert(!has_metavar(mk_pair(a, x, x)));
+    lean_assert(has_metavar(mk_pair(f(m), x, x)));
+    lean_assert(has_metavar(mk_pair(f(a), m, x)));
+    lean_assert(has_metavar(mk_pair(f(a), a, m)));
+    lean_assert(has_metavar(mk_pair(f(a), a, f(m))));
 }
 
 static void check_copy(expr const & e) {
@@ -338,6 +347,52 @@ static void tst17() {
     check_serializer(t);
 }
 
+static void tst18() {
+    expr f = Const("f");
+    expr x = Var(0);
+    expr a = Const("a");
+    expr l = mk_local("m", Bool);
+    expr m = mk_metavar("m", Bool);
+    check_serializer(l);
+    lean_assert(!has_local(m));
+    lean_assert(has_local(l));
+    lean_assert(!has_local(f(m)));
+    lean_assert(has_local(f(l)));
+    lean_assert(!has_local(f(a)));
+    lean_assert(!has_local(f(x)));
+    lean_assert(!has_local(Pi({a, Type}, a)));
+    lean_assert(!has_local(Pi({a, m}, a)));
+    lean_assert(!has_local(Type));
+    lean_assert(!has_local(Pi({a, Type}, a)));
+    lean_assert(has_local(Pi({a, Type}, l)));
+    lean_assert(!has_metavar(Pi({a, Type}, l)));
+    lean_assert(has_local(Pi({a, l}, a)));
+    lean_assert(has_local(Fun({a, Type}, l)));
+    lean_assert(has_local(Fun({a, l}, a)));
+    lean_assert(!has_local(Let(a, Type, Bool, a)));
+    lean_assert(has_local(mk_let(name("a"), l, f(x), f(f(x)))));
+    lean_assert(has_local(mk_let(name("a"), Type, f(l), f(f(x)))));
+    lean_assert(has_local(mk_let(name("a"), Type, f(x), f(f(l)))));
+    lean_assert(has_local(f(a, a, l)));
+    lean_assert(has_local(f(a, l, a, a)));
+    lean_assert(!has_local(f(a, a, a, a)));
+    lean_assert(!has_local(mk_fst(a)));
+    lean_assert(!has_local(mk_snd(a)));
+    lean_assert(has_local(mk_fst(l)));
+    lean_assert(has_local(mk_snd(l)));
+    lean_assert(!has_local(mk_fst(m)));
+    lean_assert(!has_local(mk_snd(m)));
+    lean_assert(!has_local(mk_pair(a, x, x)));
+    lean_assert(has_local(mk_pair(f(l), x, x)));
+    lean_assert(has_local(mk_pair(f(a), l, x)));
+    lean_assert(has_local(mk_pair(f(a), a, l)));
+    lean_assert(has_local(mk_pair(f(a), a, f(l))));
+    lean_assert(!has_local(mk_pair(f(m), x, x)));
+    lean_assert(!has_local(mk_pair(f(a), m, x)));
+    lean_assert(!has_local(mk_pair(f(a), a, m)));
+    lean_assert(!has_local(mk_pair(f(a), a, f(m))));
+}
+
 int main() {
     save_stack_info();
     lean_assert(sizeof(expr) == sizeof(optional<expr>));
@@ -358,6 +413,7 @@ int main() {
     tst15();
     tst16();
     tst17();
+    tst18();
     std::cout << "sizeof(expr):            " << sizeof(expr) << "\n";
     std::cout << "sizeof(expr_app):        " << sizeof(expr_app) << "\n";
     std::cout << "sizeof(expr_cell):       " << sizeof(expr_cell) << "\n";