diff --git a/src/tests/util/name.cpp b/src/tests/util/name.cpp
index 8becec283..e9c75f465 100644
--- a/src/tests/util/name.cpp
+++ b/src/tests/util/name.cpp
@@ -70,6 +70,11 @@ static void tst4() {
     lean_assert(!is_prefix_of(name{"foo"}, name{"fo", "bla", "foo"}));
     lean_assert(!is_prefix_of(name{"foo", "bla", "foo"}, name{"foo", "bla"}));
     lean_assert(is_prefix_of(name{"foo", "bla"}, name(name{"foo", "bla"}, 0u)));
+    lean_assert(is_prefix_of(name("aaa"), name("aaa")));
+    lean_assert(!is_prefix_of(name("aaa"), name("aaab")));
+    lean_assert(!is_prefix_of(name("aaab"), name("aaa")));
+    lean_assert(!is_prefix_of(name{"foo", "bla"}, name{"foo"}));
+    lean_assert(is_prefix_of(name{"foo"}, name{"foo", "bla"}));
 }
 
 static void tst5() {
@@ -157,6 +162,15 @@ static void tst12() {
     lean_assert(mk_unique(s, name("foo")) == name(name("foo"), 2));
 }
 
+static void tst13() {
+    name_generator g1("a");
+    name_generator c1 = g1.mk_child();
+    name_generator c2 = g1.mk_child();
+    lean_assert(c1.next() != c2.next());
+    std::cout << c1.next() << "\n";
+    std::cout << c2.next() << "\n";
+}
+
 int main() {
     tst1();
     tst2();
@@ -170,5 +184,6 @@ int main() {
     tst10();
     tst11();
     tst12();
+    tst13();
     return has_violations() ? 1 : 0;
 }
diff --git a/src/util/CMakeLists.txt b/src/util/CMakeLists.txt
index 02b4f32c3..b941c05e5 100644
--- a/src/util/CMakeLists.txt
+++ b/src/util/CMakeLists.txt
@@ -4,7 +4,7 @@ else()
   set(THREAD_CPP "")
 endif()
 
-add_library(util trace.cpp debug.cpp name.cpp name_set.cpp
+add_library(util trace.cpp debug.cpp name.cpp name_set.cpp name_generator.cpp
   exception.cpp interrupt.cpp hash.cpp escaped.cpp bit_tricks.cpp
   safe_arith.cpp ascii.cpp memory.cpp shared_mutex.cpp realpath.cpp
   script_state.cpp script_exception.cpp splay_map.cpp lua.cpp
diff --git a/src/util/name.cpp b/src/util/name.cpp
index 8f6c2b749..723743ae0 100644
--- a/src/util/name.cpp
+++ b/src/util/name.cpp
@@ -212,6 +212,8 @@ bool operator==(name const & a, name const & b) {
 }
 
 bool is_prefix_of(name const & n1, name const & n2) {
+    if (n2.is_atomic())
+        return n1 == n2;
     buffer<name::imp*> limbs1, limbs2;
     name::imp* i1 = n1.m_ptr;
     name::imp* i2 = n2.m_ptr;
diff --git a/src/util/name.h b/src/util/name.h
index 577ee2610..5e45674f8 100644
--- a/src/util/name.h
+++ b/src/util/name.h
@@ -129,6 +129,17 @@ struct name_eq { bool operator()(name const & n1, name const & n2) const { retur
 struct name_cmp { int operator()(name const & n1, name const & n2) const { return cmp(n1, n2); } };
 struct name_quick_cmp { int operator()(name const & n1, name const & n2) const { return quick_cmp(n1, n2); } };
 
+/**
+   \brief Return true iff the two given names are independent.
+   That \c a is not a prefix of \c b, nor \c b is a prefix of \c a
+
+   \remark forall a b c d,
+               independent(a, b) => independent(join(a, c), join(b, d))
+*/
+inline bool independent(name const & a, name const & b) {
+    return !is_prefix_of(a, b) && !is_prefix_of(b, a);
+}
+
 serializer & operator<<(serializer & s, name const & n);
 name read_name(deserializer & d);
 inline deserializer & operator>>(deserializer & d, name & n) { n = read_name(d); return d; }
diff --git a/src/util/name_generator.cpp b/src/util/name_generator.cpp
new file mode 100644
index 000000000..e8e9b58ba
--- /dev/null
+++ b/src/util/name_generator.cpp
@@ -0,0 +1,26 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include <limits>
+#include "util/name_generator.h"
+
+namespace lean {
+name name_generator::next() {
+    if (m_next_idx == std::numeric_limits<unsigned>::max()) {
+        // avoid overflow
+        m_prefix   = name(m_prefix, m_next_idx);
+        m_next_idx = 0;
+    }
+    name r(m_prefix, m_next_idx);
+    m_next_idx++;
+    return r;
+}
+
+void swap(name_generator & a, name_generator & b) {
+    swap(a.m_prefix, b.m_prefix);
+    std::swap(a.m_next_idx, b.m_next_idx);
+}
+}
diff --git a/src/util/name_generator.h b/src/util/name_generator.h
index b10813abf..ead534044 100644
--- a/src/util/name_generator.h
+++ b/src/util/name_generator.h
@@ -11,8 +11,10 @@ Author: Leonardo de Moura
 namespace lean {
 /**
    \brief A generator of unique names modulo a prefix.
-   If the prefix is unique (i.e., it is not the prefix of any other name in the system), then
-   all generated names are unique.
+   If the initial prefix is independent of all other names in the system, then all generated names are unique.
+
+   \remark There is no risk of overflow in the m_next_idx. If m_next_idx reaches std::numeric_limits<unsigned>::max(),
+   then the prefix becomes name(m_prefix, m_next_idx), and m_next_idx is reset to 0
 */
 class name_generator {
     name     m_prefix;
@@ -23,11 +25,15 @@ public:
     name const & prefix() const { return m_prefix; }
 
     /** \brief Return a unique name modulo \c prefix. */
-    name next() { name r(m_prefix, m_next_idx); m_next_idx++; return r; }
+    name next();
 
-    friend void swap(name_generator & a, name_generator & b) {
-        swap(a.m_prefix, b.m_prefix);
-        std::swap(a.m_next_idx, b.m_next_idx);
-    }
+    /**
+        \brief Create a child name_generator, each child name_generator is guaranteed to produce
+        names different from this name_generator and any other name_generator created with this generator.
+    */
+    name_generator mk_child() { return name_generator(next()); }
+
+    friend void swap(name_generator & a, name_generator & b);
 };
+void swap(name_generator & a, name_generator & b);
 }