diff --git a/src/frontends/lean/begin_end_ext.cpp b/src/frontends/lean/begin_end_ext.cpp
index 264371a3a..1a892e557 100644
--- a/src/frontends/lean/begin_end_ext.cpp
+++ b/src/frontends/lean/begin_end_ext.cpp
@@ -103,12 +103,12 @@ static void check_valid_tactic(environment const & env, expr const & pre_tac) {
 
 environment add_begin_end_pre_tactic(environment const & env, expr const & pre_tac) {
     check_valid_tactic(env, pre_tac);
-    return begin_end_ext::add_entry(env, get_dummy_ios(), be_entry(true, pre_tac));
+    return begin_end_ext::add_entry(env, get_dummy_ios(), be_entry(true, pre_tac), get_namespace(env), true);
 }
 
 environment set_begin_end_pre_tactic(environment const & env, expr const & pre_tac) {
     check_valid_tactic(env, pre_tac);
-    return begin_end_ext::add_entry(env, get_dummy_ios(), be_entry(false, pre_tac));
+    return begin_end_ext::add_entry(env, get_dummy_ios(), be_entry(false, pre_tac), get_namespace(env), true);
 }
 
 optional<expr> get_begin_end_pre_tactic(environment const & env) {
diff --git a/src/frontends/lean/decl_attributes.cpp b/src/frontends/lean/decl_attributes.cpp
index 9acfe8f0e..c8f29822c 100644
--- a/src/frontends/lean/decl_attributes.cpp
+++ b/src/frontends/lean/decl_attributes.cpp
@@ -169,7 +169,7 @@ void decl_attributes::parse(parser & p) {
     }
 }
 
-environment decl_attributes::apply(environment env, io_state const & ios, name const & d) const {
+environment decl_attributes::apply(environment env, io_state const & ios, name const & d, name const & ns) const {
     bool forward = m_forward;
     if (has_pattern_hints(env.get(d).get_type())) {
         // turn on [forward] if patterns hints have been used in the type.
@@ -181,9 +181,9 @@ environment decl_attributes::apply(environment env, io_state const & ios, name c
             #if defined(__GNUC__) && !defined(__CLANG__)
             #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
             #endif
-            env = add_instance(env, d, *m_priority, m_persistent);
+            env = add_instance(env, d, *m_priority, ns, m_persistent);
         } else {
-            env = add_instance(env, d, m_persistent);
+            env = add_instance(env, d, ns, m_persistent);
         }
     }
     if (m_is_trans_instance) {
@@ -191,75 +191,75 @@ environment decl_attributes::apply(environment env, io_state const & ios, name c
             #if defined(__GNUC__) && !defined(__CLANG__)
             #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
             #endif
-            env = add_trans_instance(env, d, *m_priority, m_persistent);
+            env = add_trans_instance(env, d, *m_priority, ns, m_persistent);
         } else {
-            env = add_trans_instance(env, d, m_persistent);
+            env = add_trans_instance(env, d, ns, m_persistent);
         }
     }
     if (m_is_coercion)
-        env = add_coercion(env, ios, d, m_persistent);
+        env = add_coercion(env, ios, d, ns, m_persistent);
     auto decl = env.find(d);
     if (decl && decl->is_definition()) {
         if (m_is_reducible)
-            env = set_reducible(env, d, reducible_status::Reducible, m_persistent);
+            env = set_reducible(env, d, reducible_status::Reducible, ns, m_persistent);
         if (m_is_irreducible)
-            env = set_reducible(env, d, reducible_status::Irreducible, m_persistent);
+            env = set_reducible(env, d, reducible_status::Irreducible, ns, m_persistent);
         if (m_is_semireducible)
-            env = set_reducible(env, d, reducible_status::Semireducible, m_persistent);
+            env = set_reducible(env, d, reducible_status::Semireducible, ns, m_persistent);
         if (m_is_quasireducible)
-            env = set_reducible(env, d, reducible_status::Quasireducible, m_persistent);
+            env = set_reducible(env, d, reducible_status::Quasireducible, ns, m_persistent);
         if (m_unfold_hint)
-            env = add_unfold_hint(env, d, m_unfold_hint, m_persistent);
+            env = add_unfold_hint(env, d, m_unfold_hint, ns, m_persistent);
         if (m_unfold_full_hint)
-            env = add_unfold_full_hint(env, d, m_persistent);
+            env = add_unfold_full_hint(env, d, ns, m_persistent);
     }
     if (m_constructor_hint)
-        env = add_constructor_hint(env, d, m_persistent);
+        env = add_constructor_hint(env, d, ns, m_persistent);
     if (m_symm)
-        env = add_symm(env, d, m_persistent);
+        env = add_symm(env, d, ns, m_persistent);
     if (m_refl)
-        env = add_refl(env, d, m_persistent);
+        env = add_refl(env, d, ns, m_persistent);
     if (m_trans)
-        env = add_trans(env, d, m_persistent);
+        env = add_trans(env, d, ns, m_persistent);
     if (m_subst)
-        env = add_subst(env, d, m_persistent);
+        env = add_subst(env, d, ns, m_persistent);
     if (m_recursor)
-        env = add_user_recursor(env, d, m_recursor_major_pos, m_persistent);
+        env = add_user_recursor(env, d, m_recursor_major_pos, ns, m_persistent);
     if (m_is_class)
-        env = add_class(env, d, m_persistent);
+        env = add_class(env, d, ns, m_persistent);
     if (m_simp) {
         if (m_priority)
-            env = add_simp_rule(env, d, *m_priority, m_persistent);
+            env = add_simp_rule(env, d, *m_priority, ns, m_persistent);
         else
-            env = add_simp_rule(env, d, LEAN_SIMP_DEFAULT_PRIORITY, m_persistent);
+            env = add_simp_rule(env, d, LEAN_SIMP_DEFAULT_PRIORITY, ns, m_persistent);
     }
     if (m_congr) {
         if (m_priority)
-            env = add_congr_rule(env, d, *m_priority, m_persistent);
+            env = add_congr_rule(env, d, *m_priority, ns, m_persistent);
         else
-            env = add_congr_rule(env, d, LEAN_SIMP_DEFAULT_PRIORITY, m_persistent);
+            env = add_congr_rule(env, d, LEAN_SIMP_DEFAULT_PRIORITY, ns, m_persistent);
     }
     if (m_light_arg) {
-        env = add_light_rule(env, d, *m_light_arg, m_persistent);
+        env = add_light_rule(env, d, *m_light_arg, ns, m_persistent);
     }
     if (m_backward) {
         if (m_priority)
-            env = add_backward_rule(env, d, *m_priority, m_persistent);
+            env = add_backward_rule(env, d, *m_priority, ns, m_persistent);
         else
-            env = add_backward_rule(env, d, LEAN_BACKWARD_DEFAULT_PRIORITY, m_persistent);
+            env = add_backward_rule(env, d, LEAN_BACKWARD_DEFAULT_PRIORITY, ns, m_persistent);
     }
     if (forward) {
         mk_multipatterns(env, ios, d); // try to create patterns
         if (m_priority)
-            env = add_forward_lemma(env, d, *m_priority, m_persistent);
+            env = add_forward_lemma(env, d, *m_priority, ns, m_persistent);
         else
-            env = add_forward_lemma(env, d, LEAN_FORWARD_LEMMA_DEFAULT_PRIORITY, m_persistent);
+            env = add_forward_lemma(env, d, LEAN_FORWARD_LEMMA_DEFAULT_PRIORITY, ns, m_persistent);
     }
     if (m_no_pattern) {
-        env = add_no_pattern(env, d, m_persistent);
+        env = add_no_pattern(env, d, ns, m_persistent);
     }
     if (m_has_multiple_instances)
-        env = mark_multiple_instances(env, d, m_persistent);
+        env = mark_multiple_instances(env, d, ns, m_persistent);
     return env;
 }
 
diff --git a/src/frontends/lean/decl_attributes.h b/src/frontends/lean/decl_attributes.h
index 2d277267c..a950ee17f 100644
--- a/src/frontends/lean/decl_attributes.h
+++ b/src/frontends/lean/decl_attributes.h
@@ -41,7 +41,7 @@ class decl_attributes {
 public:
     decl_attributes(bool is_abbrev = false, bool persistent = true);
     void parse(parser & p);
-    environment apply(environment env, io_state const & ios, name const & d) const;
+    environment apply(environment env, io_state const & ios, name const & d, name const & ns) const;
     bool is_parsing_only() const { return m_is_parsing_only; }
     void write(serializer & s) const;
     void read(deserializer & d);
diff --git a/src/frontends/lean/decl_cmds.cpp b/src/frontends/lean/decl_cmds.cpp
index 357a963e9..738a26467 100644
--- a/src/frontends/lean/decl_cmds.cpp
+++ b/src/frontends/lean/decl_cmds.cpp
@@ -906,9 +906,9 @@ class definition_cmd_fn {
             }
             if (m_kind == Abbreviation || m_kind == LocalAbbreviation) {
                 bool persistent = m_kind == Abbreviation;
-                m_env = add_abbreviation(m_env, real_n, m_attributes.is_parsing_only(), persistent);
+                m_env = add_abbreviation(m_env, real_n, m_attributes.is_parsing_only(), get_namespace(m_env), persistent);
             }
-            m_env = m_attributes.apply(m_env, m_p.ios(), real_n);
+            m_env = m_attributes.apply(m_env, m_p.ios(), real_n, get_namespace(m_env));
         }
     }
 
@@ -1260,9 +1260,18 @@ static environment attribute_cmd_core(parser & p, bool persistent) {
     bool abbrev     = false;
     decl_attributes attributes(abbrev, persistent);
     attributes.parse(p);
+    name ns = get_namespace(p.env());
+    if (p.curr_is_token(get_at_tk())) {
+        if (!persistent)
+            throw parser_error("invalid 'attribute' command, 'at' modifier cannot be used with local attributes", p.pos());
+        p.next();
+        ns = p.check_id_next("invalid 'attribute' command, identifier expected");
+        if (ns == get_root_tk())
+            ns = name();
+    }
     environment env = p.env();
     for (name const & d : ds)
-        env = attributes.apply(env, p.ios(), d);
+        env = attributes.apply(env, p.ios(), d, ns);
     return env;
 }
 
diff --git a/src/frontends/lean/inductive_cmd.cpp b/src/frontends/lean/inductive_cmd.cpp
index d682124f6..e271cbb47 100644
--- a/src/frontends/lean/inductive_cmd.cpp
+++ b/src/frontends/lean/inductive_cmd.cpp
@@ -772,7 +772,7 @@ struct inductive_cmd_fn {
     environment apply_modifiers(environment env) {
         m_modifiers.for_each([&](name const & n, modifiers const & m) {
                 if (m.is_class())
-                    env = add_class(env, n);
+                    env = add_class(env, n, get_namespace(env), true);
             });
         return env;
     }
diff --git a/src/frontends/lean/local_ref_info.cpp b/src/frontends/lean/local_ref_info.cpp
index daf56fcde..73d16a03c 100644
--- a/src/frontends/lean/local_ref_info.cpp
+++ b/src/frontends/lean/local_ref_info.cpp
@@ -53,7 +53,7 @@ typedef scoped_ext<local_ref_config> local_ref_ext;
 
 environment save_local_ref_info(environment const & env, name const & n, expr const & ref) {
     bool persistent = false;
-    return local_ref_ext::add_entry(env, get_dummy_ios(), local_ref_entry(n, ref), persistent);
+    return local_ref_ext::add_entry(env, get_dummy_ios(), local_ref_entry(n, ref), get_namespace(env), persistent);
 }
 
 optional<expr> get_local_ref_info(environment const & env, name const & n) {
diff --git a/src/frontends/lean/nested_declaration.cpp b/src/frontends/lean/nested_declaration.cpp
index a26e6b797..6c38931df 100644
--- a/src/frontends/lean/nested_declaration.cpp
+++ b/src/frontends/lean/nested_declaration.cpp
@@ -169,7 +169,7 @@ public:
         if (new_name != new_real_name)
             m_env = add_expr_alias_rec(m_env, new_name, new_real_name);
         decl_attributes const & attrs = get_nested_declaration_attributes(e);
-        m_env = attrs.apply(m_env, m_ios, new_real_name);
+        m_env = attrs.apply(m_env, m_ios, new_real_name, get_namespace(m_env));
         return mk_app(mk_constant(new_real_name, ls), locals.get_collected());
     }
 
diff --git a/src/frontends/lean/parser_config.cpp b/src/frontends/lean/parser_config.cpp
index f6376d12a..0fad9162c 100644
--- a/src/frontends/lean/parser_config.cpp
+++ b/src/frontends/lean/parser_config.cpp
@@ -115,7 +115,7 @@ template class scoped_ext<token_config>;
 typedef scoped_ext<token_config> token_ext;
 
 environment add_token(environment const & env, token_entry const & e, bool persistent) {
-    return token_ext::add_entry(env, get_dummy_ios(), e, persistent);
+    return token_ext::add_entry(env, get_dummy_ios(), e, get_namespace(env), persistent);
 }
 
 environment add_expr_token(environment const & env, char const * val, unsigned prec) {
@@ -348,7 +348,7 @@ template class scoped_ext<notation_config>;
 typedef scoped_ext<notation_config> notation_ext;
 
 environment add_notation(environment const & env, notation_entry const & e, bool persistent) {
-    return notation_ext::add_entry(env, get_dummy_ios(), e, persistent);
+    return notation_ext::add_entry(env, get_dummy_ios(), e, get_namespace(env), persistent);
 }
 
 parse_table const & get_nud_table(environment const & env) {
diff --git a/src/frontends/lean/structure_cmd.cpp b/src/frontends/lean/structure_cmd.cpp
index e5e98ea14..5835aaff8 100644
--- a/src/frontends/lean/structure_cmd.cpp
+++ b/src/frontends/lean/structure_cmd.cpp
@@ -693,7 +693,7 @@ struct structure_cmd_fn {
         add_alias(m_mk);
         add_rec_alias(rec_name);
         if (m_modifiers.is_class())
-            m_env = add_class(m_env, m_name);
+            m_env = add_class(m_env, m_name, get_namespace(m_env), true);
     }
 
     void save_def_info(name const & n) {
@@ -723,9 +723,9 @@ struct structure_cmd_fn {
         declaration new_decl = mk_definition(m_env, n, rec_on_decl.get_univ_params(),
                                              rec_on_decl.get_type(), rec_on_decl.get_value());
         m_env = module::add(m_env, check(m_env, new_decl));
-        m_env = set_reducible(m_env, n, reducible_status::Reducible);
+        m_env = set_reducible(m_env, n, reducible_status::Reducible, get_namespace(m_env), true);
         if (list<unsigned> idx = has_unfold_hint(m_env, rec_on_name))
-            m_env = add_unfold_hint(m_env, n, idx);
+            m_env = add_unfold_hint(m_env, n, idx, get_namespace(m_env), true);
         save_def_info(n);
         add_alias(n);
     }
@@ -814,15 +814,15 @@ struct structure_cmd_fn {
             bool use_conv_opt              = false;
             declaration coercion_decl      = mk_definition(m_env, coercion_name, lnames, coercion_type, coercion_value, use_conv_opt);
             m_env = module::add(m_env, check(m_env, coercion_decl));
-            m_env = set_reducible(m_env, coercion_name, reducible_status::Reducible);
+            m_env = set_reducible(m_env, coercion_name, reducible_status::Reducible, get_namespace(m_env), true);
             save_def_info(coercion_name);
             add_alias(coercion_name);
             if (!m_private_parents[i]) {
                 if (!m_modifiers.is_class() || !is_class(m_env, parent_name))
-                    m_env = add_coercion(m_env, m_p.ios(), coercion_name);
+                    m_env = add_coercion(m_env, m_p.ios(), coercion_name, get_namespace(m_env), true);
                 if (m_modifiers.is_class() && is_class(m_env, parent_name)) {
                     // if both are classes, then we also mark coercion_name as an instance
-                    m_env = add_trans_instance(m_env, coercion_name);
+                    m_env = add_trans_instance(m_env, coercion_name, get_namespace(m_env), true);
                 }
             }
         }
diff --git a/src/frontends/lean/tactic_hint.cpp b/src/frontends/lean/tactic_hint.cpp
index 761f417c8..de4321559 100644
--- a/src/frontends/lean/tactic_hint.cpp
+++ b/src/frontends/lean/tactic_hint.cpp
@@ -87,7 +87,7 @@ expr parse_tactic_name(parser & p) {
 
 environment tactic_hint_cmd(parser & p) {
     expr pre_tac = parse_tactic_name(p);
-    return tactic_hint_ext::add_entry(p.env(), get_dummy_ios(), pre_tac);
+    return tactic_hint_ext::add_entry(p.env(), get_dummy_ios(), pre_tac, get_namespace(p.env()), true);
 }
 
 void register_tactic_hint_cmd(cmd_table & r) {
diff --git a/src/library/abbreviation.cpp b/src/library/abbreviation.cpp
index 87f0b1b5c..c28ece7d3 100644
--- a/src/library/abbreviation.cpp
+++ b/src/library/abbreviation.cpp
@@ -80,8 +80,8 @@ struct abbrev_config {
 template class scoped_ext<abbrev_config>;
 typedef scoped_ext<abbrev_config> abbrev_ext;
 
-environment add_abbreviation(environment const & env, name const & n, bool parsing_only, bool persistent) {
-    return abbrev_ext::add_entry(env, get_dummy_ios(), abbrev_entry(n, parsing_only), persistent);
+environment add_abbreviation(environment const & env, name const & n, bool parsing_only, name const & ns, bool persistent) {
+    return abbrev_ext::add_entry(env, get_dummy_ios(), abbrev_entry(n, parsing_only), ns, persistent);
 }
 
 bool is_abbreviation(environment const & env, name const & n) {
diff --git a/src/library/abbreviation.h b/src/library/abbreviation.h
index 75a2d3ded..0d06c38bb 100644
--- a/src/library/abbreviation.h
+++ b/src/library/abbreviation.h
@@ -8,7 +8,7 @@ Author: Leonardo de Moura
 #include "kernel/environment.h"
 
 namespace lean {
-environment add_abbreviation(environment const & env, name const & n, bool parsing_only, bool persistent = true);
+environment add_abbreviation(environment const & env, name const & n, bool parsing_only, name const & ns, bool persistent);
 bool is_abbreviation(environment const & env, name const & n);
 bool is_parsing_only_abbreviation(environment const & env, name const & n);
 optional<name> is_abbreviated(environment const & env, expr const & e);
diff --git a/src/library/blast/backward/backward_rule_set.cpp b/src/library/blast/backward/backward_rule_set.cpp
index d4470dd04..18cd5ffe3 100644
--- a/src/library/blast/backward/backward_rule_set.cpp
+++ b/src/library/blast/backward/backward_rule_set.cpp
@@ -63,8 +63,8 @@ struct brs_config {
 template class scoped_ext<brs_config>;
 typedef scoped_ext<brs_config> brs_ext;
 
-environment add_backward_rule(environment const & env, name const & n, unsigned priority,  bool persistent) {
-    return brs_ext::add_entry(env, get_dummy_ios(), brs_entry(n, priority), persistent);
+environment add_backward_rule(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent) {
+    return brs_ext::add_entry(env, get_dummy_ios(), brs_entry(n, priority), ns, persistent);
 }
 
 bool is_backward_rule(environment const & env, name const & n) {
diff --git a/src/library/blast/backward/backward_rule_set.h b/src/library/blast/backward/backward_rule_set.h
index 6c27166b0..dd1a921b2 100644
--- a/src/library/blast/backward/backward_rule_set.h
+++ b/src/library/blast/backward/backward_rule_set.h
@@ -53,7 +53,7 @@ void initialize_backward_rule_set();
 void finalize_backward_rule_set();
 }
 
-environment add_backward_rule(environment const & env, name const & n, unsigned priority, bool persistent);
+environment add_backward_rule(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent);
 
 /** \brief Return true if \c n is an active backward rule in \c env */
 bool is_backward_rule(environment const & env, name const & n);
diff --git a/src/library/blast/forward/forward_lemma_set.cpp b/src/library/blast/forward/forward_lemma_set.cpp
index 32dcd7920..1b312f76f 100644
--- a/src/library/blast/forward/forward_lemma_set.cpp
+++ b/src/library/blast/forward/forward_lemma_set.cpp
@@ -53,8 +53,8 @@ struct forward_lemma_set_config {
 template class scoped_ext<forward_lemma_set_config>;
 typedef scoped_ext<forward_lemma_set_config> forward_lemma_set_ext;
 
-environment add_forward_lemma(environment const & env, name const & n, unsigned priority, bool persistent) {
-    return forward_lemma_set_ext::add_entry(env, get_dummy_ios(), forward_lemma(n, priority), persistent);
+environment add_forward_lemma(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent) {
+    return forward_lemma_set_ext::add_entry(env, get_dummy_ios(), forward_lemma(n, priority), ns, persistent);
 }
 
 bool is_forward_lemma(environment const & env, name const & n) {
diff --git a/src/library/blast/forward/forward_lemma_set.h b/src/library/blast/forward/forward_lemma_set.h
index b357fb9d2..98e45efb1 100644
--- a/src/library/blast/forward/forward_lemma_set.h
+++ b/src/library/blast/forward/forward_lemma_set.h
@@ -16,7 +16,7 @@ namespace lean {
 /** \brief The forward lemma set is actually a mapping from lemma name to priority */
 typedef rb_map<name, unsigned, name_quick_cmp> forward_lemma_set;
 
-environment add_forward_lemma(environment const & env, name const & n, unsigned priority, bool persistent);
+environment add_forward_lemma(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent);
 bool is_forward_lemma(environment const & env, name const & n);
 forward_lemma_set get_forward_lemma_set(environment const & env);
 
diff --git a/src/library/blast/forward/pattern.cpp b/src/library/blast/forward/pattern.cpp
index deabf091d..c4d13e6fc 100644
--- a/src/library/blast/forward/pattern.cpp
+++ b/src/library/blast/forward/pattern.cpp
@@ -175,8 +175,8 @@ bool is_no_pattern(environment const & env, name const & n) {
     return no_pattern_ext::get_state(env).contains(n);
 }
 
-environment add_no_pattern(environment const & env, name const & n, bool persistent) {
-    return no_pattern_ext::add_entry(env, get_dummy_ios(), n, persistent);
+environment add_no_pattern(environment const & env, name const & n, name const & ns, bool persistent) {
+    return no_pattern_ext::add_entry(env, get_dummy_ios(), n, ns, persistent);
 }
 
 name_set const & get_no_patterns(environment const & env) {
diff --git a/src/library/blast/forward/pattern.h b/src/library/blast/forward/pattern.h
index 66a1ed1b6..b7109e633 100644
--- a/src/library/blast/forward/pattern.h
+++ b/src/library/blast/forward/pattern.h
@@ -22,7 +22,7 @@ bool has_pattern_hints(expr const & e);
 
 /** \brief Hint for the pattern inference procedure.
     It should not consider/infer patterns containing the constant \c n. */
-environment add_no_pattern(environment const & env, name const & n, bool persistent);
+environment add_no_pattern(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Return true if constant \c n is marked as [no_pattern] in the given environment. */
 bool is_no_pattern(environment const & env, name const & n);
 /** \brief Return the set of constants marked as no-patterns */
diff --git a/src/library/blast/simplifier/simp_rule_set.cpp b/src/library/blast/simplifier/simp_rule_set.cpp
index e2f4e5d33..db2a7b394 100644
--- a/src/library/blast/simplifier/simp_rule_set.cpp
+++ b/src/library/blast/simplifier/simp_rule_set.cpp
@@ -524,12 +524,12 @@ struct rrs_config {
 template class scoped_ext<rrs_config>;
 typedef scoped_ext<rrs_config> rrs_ext;
 
-environment add_simp_rule(environment const & env, name const & n, unsigned prio, bool persistent) {
-    return rrs_ext::add_entry(env, get_dummy_ios(), rrs_entry(true, n, prio), persistent);
+environment add_simp_rule(environment const & env, name const & n, unsigned prio, name const & ns, bool persistent) {
+    return rrs_ext::add_entry(env, get_dummy_ios(), rrs_entry(true, n, prio), ns, persistent);
 }
 
-environment add_congr_rule(environment const & env, name const & n, unsigned prio, bool persistent) {
-    return rrs_ext::add_entry(env, get_dummy_ios(), rrs_entry(false, n, prio), persistent);
+environment add_congr_rule(environment const & env, name const & n, unsigned prio, name const & ns, bool persistent) {
+    return rrs_ext::add_entry(env, get_dummy_ios(), rrs_entry(false, n, prio), ns, persistent);
 }
 
 bool is_simp_rule(environment const & env, name const & n) {
diff --git a/src/library/blast/simplifier/simp_rule_set.h b/src/library/blast/simplifier/simp_rule_set.h
index 0c812d1cf..07c47eefa 100644
--- a/src/library/blast/simplifier/simp_rule_set.h
+++ b/src/library/blast/simplifier/simp_rule_set.h
@@ -134,8 +134,8 @@ public:
 simp_rule_sets add(tmp_type_context & tctx, simp_rule_sets const & s, name const & id, expr const & e, expr const & h, unsigned priority);
 simp_rule_sets join(simp_rule_sets const & s1, simp_rule_sets const & s2);
 
-environment add_simp_rule(environment const & env, name const & n, unsigned priority,  bool persistent);
-environment add_congr_rule(environment const & env, name const & n, unsigned priority, bool persistent);
+environment add_simp_rule(environment const & env, name const & n, unsigned priority,  name const & ns, bool persistent);
+environment add_congr_rule(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent);
 
 /** \brief Return true if \c n is an active simplification rule in \c env */
 bool is_simp_rule(environment const & env, name const & n);
diff --git a/src/library/class.cpp b/src/library/class.cpp
index 7d7d0363a..3c0d333fc 100644
--- a/src/library/class.cpp
+++ b/src/library/class.cpp
@@ -235,9 +235,9 @@ name get_class_name(environment const & env, expr const & e) {
     return c_name;
 }
 
-environment add_class(environment const & env, name const & n, bool persistent) {
+environment add_class(environment const & env, name const & n, name const & ns, bool persistent) {
     check_class(env, n);
-    environment new_env = class_ext::add_entry(env, get_dummy_ios(), class_entry(n), persistent);
+    environment new_env = class_ext::add_entry(env, get_dummy_ios(), class_entry(n), ns, persistent);
     return mark_class_instance_somewhere(new_env, n);
 }
 
@@ -262,7 +262,7 @@ type_checker_ptr mk_class_type_checker(environment const & env, name_generator &
 }
 
 static name * g_tmp_prefix = nullptr;
-environment add_instance(environment const & env, name const & n, unsigned priority, bool persistent) {
+environment add_instance(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent) {
     declaration d = env.get(n);
     expr type = d.get_type();
     name_generator ngen(*g_tmp_prefix);
@@ -275,12 +275,13 @@ environment add_instance(environment const & env, name const & n, unsigned prior
     }
     name c = get_class_name(env, get_app_fn(type));
     check_is_class(env, c);
-    environment new_env = class_ext::add_entry(env, get_dummy_ios(), class_entry(class_entry_kind::Instance, c, n, priority), persistent);
+    environment new_env = class_ext::add_entry(env, get_dummy_ios(), class_entry(class_entry_kind::Instance, c, n, priority),
+                                               ns, persistent);
     return mark_class_instance_somewhere(new_env, n);
 }
 
-environment add_instance(environment const & env, name const & n, bool persistent) {
-    return add_instance(env, n, LEAN_INSTANCE_DEFAULT_PRIORITY, persistent);
+environment add_instance(environment const & env, name const & n, name const & ns, bool persistent) {
+    return add_instance(env, n, LEAN_INSTANCE_DEFAULT_PRIORITY, ns, persistent);
 }
 
 static name * g_source = nullptr;
@@ -307,7 +308,7 @@ static pair<name, name> get_source_target(environment const & env, type_checker
     return mk_pair(*src, *tgt);
 }
 
-environment add_trans_instance(environment const & env, name const & n, unsigned priority, bool persistent) {
+environment add_trans_instance(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent) {
     type_checker_ptr  tc     = mk_type_checker(env, name_generator());
     pair<name, name> src_tgt = get_source_target(env, *tc, n);
     class_state const & s = class_ext::get_state(env);
@@ -315,25 +316,25 @@ environment add_trans_instance(environment const & env, name const & n, unsigned
     pair<environment, list<tc_edge>> new_env_insts = g.add(env, src_tgt.first, n, src_tgt.second);
     environment new_env = new_env_insts.first;
     new_env = class_ext::add_entry(new_env, get_dummy_ios(),
-                                   class_entry::mk_trans_inst(src_tgt.first, src_tgt.second, n, priority), persistent);
+                                   class_entry::mk_trans_inst(src_tgt.first, src_tgt.second, n, priority), ns, persistent);
     new_env = mark_class_instance_somewhere(new_env, n);
     for (tc_edge const & edge : new_env_insts.second) {
         new_env = class_ext::add_entry(new_env, get_dummy_ios(),
-                                       class_entry::mk_derived_trans_inst(edge.m_from, edge.m_to, edge.m_cnst), persistent);
-        new_env = set_reducible(new_env, edge.m_cnst, reducible_status::Reducible, persistent);
+                                       class_entry::mk_derived_trans_inst(edge.m_from, edge.m_to, edge.m_cnst), ns, persistent);
+        new_env = set_reducible(new_env, edge.m_cnst, reducible_status::Reducible, ns, persistent);
         new_env = add_protected(new_env, edge.m_cnst);
         new_env = mark_class_instance_somewhere(new_env, edge.m_cnst);
     }
     return new_env;
 }
 
-environment add_trans_instance(environment const & env, name const & n, bool persistent) {
-    return add_trans_instance(env, n, LEAN_INSTANCE_DEFAULT_PRIORITY, persistent);
+environment add_trans_instance(environment const & env, name const & n, name const & ns, bool persistent) {
+    return add_trans_instance(env, n, LEAN_INSTANCE_DEFAULT_PRIORITY, ns, persistent);
 }
 
-environment mark_multiple_instances(environment const & env, name const & n, bool persistent) {
+environment mark_multiple_instances(environment const & env, name const & n, name const & ns, bool persistent) {
     check_class(env, n);
-    return class_ext::add_entry(env, get_dummy_ios(), class_entry(n, true), persistent);
+    return class_ext::add_entry(env, get_dummy_ios(), class_entry(n, true), ns, persistent);
 }
 
 bool try_multiple_instances(environment const & env, name const & n) {
diff --git a/src/library/class.h b/src/library/class.h
index 71b34d70d..9cb4b7152 100644
--- a/src/library/class.h
+++ b/src/library/class.h
@@ -10,15 +10,15 @@ namespace lean {
 /** \brief Create type checker that treats classes as opaque constants */
 type_checker_ptr mk_class_type_checker(environment const & env, name_generator && ngen, bool conservative);
 /** \brief Add a new 'class' to the environment (if it is not already declared) */
-environment add_class(environment const & env, name const & n, bool persistent = true);
+environment add_class(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Add a new 'class instance' to the environment with default priority. */
-environment add_instance(environment const & env, name const & n, bool persistent = true);
+environment add_instance(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Add a new 'class instance' to the environment. */
-environment add_instance(environment const & env, name const & n, unsigned priority, bool persistent);
+environment add_instance(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent);
 /** \brief Add a new 'class transitive instance' to the environment with default priority. */
-environment add_trans_instance(environment const & env, name const & n, bool persistent = true);
+environment add_trans_instance(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Add a new 'class transitive instance' to the environment. */
-environment add_trans_instance(environment const & env, name const & n, unsigned priority, bool persistent);
+environment add_trans_instance(environment const & env, name const & n, unsigned priority, name const & ns, bool persistent);
 /** \brief Return true iff \c c was declared with \c add_class. */
 bool is_class(environment const & env, name const & c);
 /** \brief Return true iff \c i was declared with \c add_instance. */
@@ -38,7 +38,7 @@ void get_classes(environment const & env, buffer<name> & classes);
 name get_class_name(environment const & env, expr const & e);
 
 /** \brief Mark that multiple instances of class \c n must be explored. */
-environment mark_multiple_instances(environment const & env, name const & n, bool persistent);
+environment mark_multiple_instances(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Return true iff multiple instances of class \c n must be explored. */
 bool try_multiple_instances(environment const & env, name const & n);
 
diff --git a/src/library/coercion.cpp b/src/library/coercion.cpp
index 72cc73b50..f2d4e0c0a 100644
--- a/src/library/coercion.cpp
+++ b/src/library/coercion.cpp
@@ -310,22 +310,22 @@ static unsigned get_num_args(environment const & env, tc_edge const & new_coe) {
 
 static environment add_coercion_core(environment const & env,
                                      name const & from, name const & coe, unsigned num_args, name const & to,
-                                     bool persistent) {
+                                     name const & ns, bool persistent) {
     coercion_state st = coercion_ext::get_state(env);
     pair<environment, list<tc_edge>> new_env_coes = st.m_graph.add(env, from, coe, to);
     environment new_env = new_env_coes.first;
-    new_env = coercion_ext::add_entry(new_env, get_dummy_ios(), coercion_entry(from, coe, num_args, to), persistent);
+    new_env = coercion_ext::add_entry(new_env, get_dummy_ios(), coercion_entry(from, coe, num_args, to), ns, persistent);
     for (tc_edge const & new_coe : new_env_coes.second) {
         unsigned nargs = get_num_args(new_env, new_coe);
         new_env = coercion_ext::add_entry(new_env, get_dummy_ios(),
-                                          coercion_entry(new_coe.m_from, new_coe.m_cnst, nargs, new_coe.m_to), persistent);
-        new_env = set_reducible(new_env, new_coe.m_cnst, reducible_status::Reducible, persistent);
+                                          coercion_entry(new_coe.m_from, new_coe.m_cnst, nargs, new_coe.m_to), ns, persistent);
+        new_env = set_reducible(new_env, new_coe.m_cnst, reducible_status::Reducible, ns, persistent);
         new_env = add_protected(new_env, new_coe.m_cnst);
     }
     return new_env;
 }
 
-static environment add_coercion(environment const & env, name const & f, name const & C, bool persistent) {
+static environment add_coercion(environment const & env, name const & f, name const & C, name const & ns, bool persistent) {
     declaration d = env.get(f);
     unsigned num = 0;
     buffer<expr> args;
@@ -346,7 +346,7 @@ static environment add_coercion(environment const & env, name const & f, name co
                                 << "D t_1 ... t_m\n" << "Type\n" << "Pi x : A, B x\n");
             else if (is_user_class(*cls) && *cls == C)
                 throw exception(sstream() << "invalid coercion, '" << f << "' is a coercion from '" << C << "' to itself");
-            return add_coercion_core(env, C, f, num, *cls, persistent);
+            return add_coercion_core(env, C, f, num, *cls, ns, persistent);
         }
         t = binding_body(t);
         num++;
@@ -354,7 +354,7 @@ static environment add_coercion(environment const & env, name const & f, name co
     }
 }
 
-environment add_coercion(environment const & env, io_state const &, name const & f, bool persistent) {
+environment add_coercion(environment const & env, io_state const &, name const & f, name const & ns, bool persistent) {
     declaration d = env.get(f);
     expr t = d.get_type();
     check_pi(f, t);
@@ -374,10 +374,10 @@ environment add_coercion(environment const & env, io_state const &, name const &
         --i;
         if (i == 0) {
             // last alternative
-            return add_coercion(env, f, Cs[i], persistent);
+            return add_coercion(env, f, Cs[i], ns, persistent);
         } else {
             try {
-                return add_coercion(env, f, Cs[i], persistent);
+                return add_coercion(env, f, Cs[i], ns, persistent);
             } catch (exception &) {
                 // failed, keep trying...
             }
diff --git a/src/library/coercion.h b/src/library/coercion.h
index 8fc3c29fc..dfe44fea5 100644
--- a/src/library/coercion.h
+++ b/src/library/coercion.h
@@ -38,7 +38,7 @@ namespace lean {
 
    \remark if persistent == true, then coercion is saved in .olean files
 */
-environment add_coercion(environment const & env, io_state const & ios, name const & f, bool persistent = true);
+environment add_coercion(environment const & env, io_state const & ios, name const & f, name const & ns, bool persistent);
 /** \brief If \c f is a coercion, then return the name of the 'from-class' and the number of
     class parameters.
 */
diff --git a/src/library/definitional/brec_on.cpp b/src/library/definitional/brec_on.cpp
index 282edd865..66e40d7c2 100644
--- a/src/library/definitional/brec_on.cpp
+++ b/src/library/definitional/brec_on.cpp
@@ -17,6 +17,7 @@ Author: Leonardo de Moura
 #include "library/util.h"
 #include "library/normalize.h"
 #include "library/aux_recursors.h"
+#include "library/scoped_ext.h"
 
 namespace lean {
 static void throw_corrupted(name const & n) {
@@ -146,9 +147,9 @@ static environment mk_below(environment const & env, name const & n, bool ibelow
     declaration new_d = mk_definition(env, below_name, blvls, below_type, below_value,
                                       use_conv_opt);
     environment new_env = module::add(env, check(env, new_d));
-    new_env = set_reducible(new_env, below_name, reducible_status::Reducible);
+    new_env = set_reducible(new_env, below_name, reducible_status::Reducible, get_namespace(new_env), true);
     if (!ibelow)
-        new_env = add_unfold_hint(new_env, below_name, nparams + nindices + ntypeformers);
+        new_env = add_unfold_hint(new_env, below_name, nparams + nindices + ntypeformers, get_namespace(new_env), true);
     return add_protected(new_env, below_name);
 }
 
@@ -332,9 +333,9 @@ static environment mk_brec_on(environment const & env, name const & n, bool ind)
     declaration new_d = mk_definition(env, brec_on_name, blps, brec_on_type, brec_on_value,
                                       use_conv_opt);
     environment new_env = module::add(env, check(env, new_d));
-    new_env = set_reducible(new_env, brec_on_name, reducible_status::Reducible);
+    new_env = set_reducible(new_env, brec_on_name, reducible_status::Reducible, get_namespace(new_env), true);
     if (!ind)
-        new_env = add_unfold_hint(new_env, brec_on_name, nparams + nindices + ntypeformers);
+        new_env = add_unfold_hint(new_env, brec_on_name, nparams + nindices + ntypeformers, get_namespace(new_env), true);
     new_env = add_aux_recursor(new_env, brec_on_name);
     return add_protected(new_env, brec_on_name);
 }
diff --git a/src/library/definitional/cases_on.cpp b/src/library/definitional/cases_on.cpp
index 725b26847..858eb1c34 100644
--- a/src/library/definitional/cases_on.cpp
+++ b/src/library/definitional/cases_on.cpp
@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "library/constants.h"
 #include "library/normalize.h"
 #include "library/aux_recursors.h"
+#include "library/scoped_ext.h"
 
 namespace lean {
 static void throw_corrupted(name const & n) {
@@ -182,8 +183,8 @@ environment mk_cases_on(environment const & env, name const & n) {
     declaration new_d = mk_definition(env, cases_on_name, rec_decl.get_univ_params(), cases_on_type, cases_on_value,
                                       use_conv_opt);
     environment new_env = module::add(env, check(env, new_d));
-    new_env = set_reducible(new_env, cases_on_name, reducible_status::Reducible);
-    new_env = add_unfold_hint(new_env, cases_on_name, cases_on_major_idx);
+    new_env = set_reducible(new_env, cases_on_name, reducible_status::Reducible, get_namespace(new_env), true);
+    new_env = add_unfold_hint(new_env, cases_on_name, cases_on_major_idx, get_namespace(new_env), true);
     new_env = add_aux_recursor(new_env, cases_on_name);
     return add_protected(new_env, cases_on_name);
 }
diff --git a/src/library/definitional/no_confusion.cpp b/src/library/definitional/no_confusion.cpp
index fb783272d..2f353fbd7 100644
--- a/src/library/definitional/no_confusion.cpp
+++ b/src/library/definitional/no_confusion.cpp
@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "library/reducible.h"
 #include "library/constants.h"
 #include "library/normalize.h"
+#include "library/scoped_ext.h"
 
 namespace lean {
 static void throw_corrupted(name const & n) {
@@ -139,7 +140,7 @@ optional<environment> mk_no_confusion_type(environment const & env, name const &
     declaration new_d = mk_definition(env, no_confusion_type_name, lps, no_confusion_type_type, no_confusion_type_value,
                                       use_conv_opt);
     environment new_env = module::add(env, check(env, new_d));
-    new_env = set_reducible(new_env, no_confusion_type_name, reducible_status::Reducible);
+    new_env = set_reducible(new_env, no_confusion_type_name, reducible_status::Reducible, get_namespace(new_env), true);
     return some(add_protected(new_env, no_confusion_type_name));
 }
 
@@ -274,8 +275,8 @@ environment mk_no_confusion(environment const & env, name const & n) {
     declaration new_d = mk_definition(new_env, no_confusion_name, lps, no_confusion_ty, no_confusion_val,
                                       use_conv_opt);
     new_env = module::add(new_env, check(new_env, new_d));
-    new_env = set_reducible(new_env, no_confusion_name, reducible_status::Reducible);
-    new_env = add_unfold_hint(new_env, no_confusion_name, unfold_hint_idx);
+    new_env = set_reducible(new_env, no_confusion_name, reducible_status::Reducible, get_namespace(env), true);
+    new_env = add_unfold_hint(new_env, no_confusion_name, unfold_hint_idx, get_namespace(env), true);
     return add_protected(new_env, no_confusion_name);
 }
 }
diff --git a/src/library/definitional/projection.cpp b/src/library/definitional/projection.cpp
index f6aa731b8..055c83fbb 100644
--- a/src/library/definitional/projection.cpp
+++ b/src/library/definitional/projection.cpp
@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "library/module.h"
 #include "library/util.h"
 #include "library/normalize.h"
+#include "library/scoped_ext.h"
 #include "library/kernel_serializer.h"
 #include "library/definitional/projection.h"
 
@@ -257,8 +258,8 @@ environment mk_projections(environment const & env, name const & n, buffer<name>
         declaration new_d = mk_definition(env, proj_name, lvl_params, proj_type, proj_val,
                                           use_conv_opt);
         new_env = module::add(new_env, check(new_env, new_d));
-        new_env = set_reducible(new_env, proj_name, reducible_status::Reducible);
-        new_env = add_unfold_hint(new_env, proj_name, nparams);
+        new_env = set_reducible(new_env, proj_name, reducible_status::Reducible, get_namespace(env), true);
+        new_env = add_unfold_hint(new_env, proj_name, nparams, get_namespace(env), true);
         new_env = save_projection_info(new_env, proj_name, inductive::intro_rule_name(intro), nparams, i, inst_implicit);
         expr proj         = mk_app(mk_app(mk_constant(proj_name, lvls), params), c);
         intro_type        = instantiate(binding_body(intro_type), proj);
diff --git a/src/library/definitional/rec_on.cpp b/src/library/definitional/rec_on.cpp
index a2ecc09f6..83966e2e8 100644
--- a/src/library/definitional/rec_on.cpp
+++ b/src/library/definitional/rec_on.cpp
@@ -15,6 +15,7 @@ Author: Leonardo de Moura
 #include "library/protected.h"
 #include "library/normalize.h"
 #include "library/aux_recursors.h"
+#include "library/scoped_ext.h"
 
 namespace lean {
 environment mk_rec_on(environment const & env, name const & n) {
@@ -58,8 +59,8 @@ environment mk_rec_on(environment const & env, name const & n) {
     environment new_env = module::add(env,
                                       check(env, mk_definition(env, rec_on_name, rec_decl.get_univ_params(),
                                                                rec_on_type, rec_on_val, use_conv_opt)));
-    new_env = set_reducible(new_env, rec_on_name, reducible_status::Reducible);
-    new_env = add_unfold_hint(new_env, rec_on_name, rec_on_major_idx);
+    new_env = set_reducible(new_env, rec_on_name, reducible_status::Reducible, get_namespace(env), true);
+    new_env = add_unfold_hint(new_env, rec_on_name, rec_on_major_idx, get_namespace(env), true);
     new_env = add_aux_recursor(new_env, rec_on_name);
     return add_protected(new_env, rec_on_name);
 }
diff --git a/src/library/light_lt_manager.cpp b/src/library/light_lt_manager.cpp
index 84d1d9f98..2cd0ae9e9 100644
--- a/src/library/light_lt_manager.cpp
+++ b/src/library/light_lt_manager.cpp
@@ -156,8 +156,8 @@ struct lrs_config {
 template class scoped_ext<lrs_config>;
 typedef scoped_ext<lrs_config> lrs_ext;
 
-environment add_light_rule(environment const & env, name const & id, unsigned light_arg,  bool persistent) {
-    return lrs_ext::add_entry(env, get_dummy_ios(), lrs_entry(id, light_arg), persistent);
+environment add_light_rule(environment const & env, name const & id, unsigned light_arg, name const & ns, bool persistent) {
+    return lrs_ext::add_entry(env, get_dummy_ios(), lrs_entry(id, light_arg), ns, persistent);
 }
 
 optional<unsigned> is_light_rule(environment const & env, name const & n) {
diff --git a/src/library/light_lt_manager.h b/src/library/light_lt_manager.h
index 1f84ecb21..296d24ed1 100644
--- a/src/library/light_lt_manager.h
+++ b/src/library/light_lt_manager.h
@@ -13,7 +13,7 @@ namespace lean {
 
 typedef name_map<unsigned> light_rule_set;
 
-environment add_light_rule(environment const & env, name const & id, unsigned light_arg,  bool persistent);
+environment add_light_rule(environment const & env, name const & id, unsigned light_arg, name const & ns, bool persistent);
 optional<unsigned> is_light_rule(environment const & env, name const & n);
 light_rule_set get_light_rule_set(environment const & env);
 light_rule_set get_light_rule_set(environment const & env, io_state const & ios, name const & ns);
diff --git a/src/library/normalize.cpp b/src/library/normalize.cpp
index cac62e97b..7d306c957 100644
--- a/src/library/normalize.cpp
+++ b/src/library/normalize.cpp
@@ -111,12 +111,12 @@ struct unfold_hint_config {
 template class scoped_ext<unfold_hint_config>;
 typedef scoped_ext<unfold_hint_config> unfold_hint_ext;
 
-environment add_unfold_hint(environment const & env, name const & n, list<unsigned> const & idxs, bool persistent) {
+environment add_unfold_hint(environment const & env, name const & n, list<unsigned> const & idxs, name const & ns, bool persistent) {
     lean_assert(idxs);
     declaration const & d = env.get(n);
     if (!d.is_definition())
         throw exception("invalid [unfold] hint, declaration must be a non-opaque definition");
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_entry(n, idxs), persistent);
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_entry(n, idxs), ns, persistent);
 }
 
 list<unsigned> has_unfold_hint(environment const & env, name const & d) {
@@ -127,15 +127,15 @@ list<unsigned> has_unfold_hint(environment const & env, name const & d) {
         return list<unsigned>();
 }
 
-environment erase_unfold_hint(environment const & env, name const & n, bool persistent) {
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_entry(n), persistent);
+environment erase_unfold_hint(environment const & env, name const & n, name const & ns, bool persistent) {
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_entry(n), ns, persistent);
 }
 
-environment add_unfold_full_hint(environment const & env, name const & n, bool persistent) {
+environment add_unfold_full_hint(environment const & env, name const & n, name const & ns, bool persistent) {
     declaration const & d = env.get(n);
     if (!d.is_definition())
         throw exception("invalid [unfold_full] hint, declaration must be a non-opaque definition");
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_full_entry(n), persistent);
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_full_entry(n), ns, persistent);
 }
 
 bool has_unfold_full_hint(environment const & env, name const & d) {
@@ -143,13 +143,13 @@ bool has_unfold_full_hint(environment const & env, name const & d) {
     return s.m_unfold_full.contains(d);
 }
 
-environment erase_unfold_full_hint(environment const & env, name const & n, bool persistent) {
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_full_entry(n), persistent);
+environment erase_unfold_full_hint(environment const & env, name const & n, name const & ns, bool persistent) {
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_full_entry(n), ns, persistent);
 }
 
-environment add_constructor_hint(environment const & env, name const & n, bool persistent) {
+environment add_constructor_hint(environment const & env, name const & n, name const & ns, bool persistent) {
     env.get(n);
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_constructor_entry(n), persistent);
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_constructor_entry(n), ns, persistent);
 }
 
 bool has_constructor_hint(environment const & env, name const & d) {
@@ -157,8 +157,8 @@ bool has_constructor_hint(environment const & env, name const & d) {
     return s.m_constructor.contains(d);
 }
 
-environment erase_constructor_hint(environment const & env, name const & n, bool persistent) {
-    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_constructor_entry(n), persistent);
+environment erase_constructor_hint(environment const & env, name const & n, name const & ns, bool persistent) {
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_constructor_entry(n), ns, persistent);
 }
 
 void initialize_normalize() {
diff --git a/src/library/normalize.h b/src/library/normalize.h
index 18ab7d975..afd7ae1b8 100644
--- a/src/library/normalize.h
+++ b/src/library/normalize.h
@@ -40,26 +40,26 @@ expr normalize(type_checker & tc, expr const & e, std::function<bool(expr const&
 
     Of course, kernel opaque constants are not unfolded.
 */
-environment add_unfold_hint(environment const & env, name const & n, list<unsigned> const & idxs, bool persistent = true);
-inline environment add_unfold_hint(environment const & env, name const & n, unsigned idx, bool persistent = true) {
-    return add_unfold_hint(env, n, to_list(idx), persistent);
+environment add_unfold_hint(environment const & env, name const & n, list<unsigned> const & idxs, name const & ns, bool persistent);
+inline environment add_unfold_hint(environment const & env, name const & n, unsigned idx, name const & ns, bool persistent) {
+    return add_unfold_hint(env, n, to_list(idx), ns, persistent);
 }
-environment erase_unfold_hint(environment const & env, name const & n, bool persistent = true);
+environment erase_unfold_hint(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Retrieve the hint added with the procedure add_unfold_hint. */
 list<unsigned> has_unfold_hint(environment const & env, name const & d);
 
 /** \brief [unfold-full] hint instructs normalizer (and simplifier) that function application
     (f a_1 ... a_n) should be unfolded when it is fully applied */
-environment add_unfold_full_hint(environment const & env, name const & n, bool persistent = true);
-environment erase_unfold_full_hint(environment const & env, name const & n, bool persistent = true);
+environment add_unfold_full_hint(environment const & env, name const & n, name const & ns, bool persistent);
+environment erase_unfold_full_hint(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Retrieve the hint added with the procedure add_unfold_full_hint. */
 optional<unsigned> has_unfold_full_hint(environment const & env, name const & d);
 
 
 /** \brief unfold-m hint instructs normalizer (and simplifier) that function application
     (f ...) should be unfolded when it is the major premise of a constructor like operator */
-environment add_constructor_hint(environment const & env, name const & n, bool persistent = true);
-environment erase_constructor_hint(environment const & env, name const & n, bool persistent = true);
+environment add_constructor_hint(environment const & env, name const & n, name const & ns, bool persistent);
+environment erase_constructor_hint(environment const & env, name const & n, name const & ns, bool persistent);
 /** \brief Retrieve the hint added with the procedure add_constructor_hint. */
 optional<unsigned> has_constructor_hint(environment const & env, name const & d);
 
diff --git a/src/library/reducible.cpp b/src/library/reducible.cpp
index 5e977b39f..bbf1404bd 100644
--- a/src/library/reducible.cpp
+++ b/src/library/reducible.cpp
@@ -89,9 +89,9 @@ static void check_declaration(environment const & env, name const & n) {
         throw exception(sstream() << "invalid reducible command, '" << n << "' is not a definition");
 }
 
-environment set_reducible(environment const & env, name const & n, reducible_status s, bool persistent) {
+environment set_reducible(environment const & env, name const & n, reducible_status s, name const & ns, bool persistent) {
     check_declaration(env, n);
-    return reducible_ext::add_entry(env, get_dummy_ios(), reducible_entry(s, n), persistent);
+    return reducible_ext::add_entry(env, get_dummy_ios(), reducible_entry(s, n), ns, persistent);
 }
 
 reducible_status get_reducible_status(environment const & env, name const & n) {
@@ -184,13 +184,15 @@ static int mk_non_irreducible_type_checker(lua_State * L) {
 
 static int set_reducible(lua_State * L) {
     int nargs = lua_gettop(L);
+    environment const & env = to_environment(L, 1);
     if (nargs == 3) {
-        return push_environment(L, set_reducible(to_environment(L, 1), to_name_ext(L, 2),
-                                                 static_cast<reducible_status>(lua_tonumber(L, 3))));
-    } else {
-        return push_environment(L, set_reducible(to_environment(L, 1), to_name_ext(L, 2),
+        return push_environment(L, set_reducible(env, to_name_ext(L, 2),
                                                  static_cast<reducible_status>(lua_tonumber(L, 3)),
-                                                 lua_toboolean(L, 4)));
+                                                 get_namespace(env), true));
+    } else {
+        return push_environment(L, set_reducible(env, to_name_ext(L, 2),
+                                                 static_cast<reducible_status>(lua_tonumber(L, 3)),
+                                                 get_namespace(env), lua_toboolean(L, 4)));
     }
 }
 
diff --git a/src/library/reducible.h b/src/library/reducible.h
index 5d59806ab..04de65fa7 100644
--- a/src/library/reducible.h
+++ b/src/library/reducible.h
@@ -21,7 +21,7 @@ enum class reducible_status { Reducible, Quasireducible, Semireducible, Irreduci
     "Reducible" definitions can be freely unfolded by automation (i.e., elaborator, simplifier, etc).
     We should view it as a hint to automation.
 */
-environment set_reducible(environment const & env, name const & n, reducible_status s, bool persistent = true);
+environment set_reducible(environment const & env, name const & n, reducible_status s, name const & ns, bool persistent);
 
 reducible_status get_reducible_status(environment const & env, name const & n);
 
diff --git a/src/library/relation_manager.cpp b/src/library/relation_manager.cpp
index 7562de887..28f2a96ab 100644
--- a/src/library/relation_manager.cpp
+++ b/src/library/relation_manager.cpp
@@ -185,24 +185,24 @@ struct rel_config {
 template class scoped_ext<rel_config>;
 typedef scoped_ext<rel_config> rel_ext;
 
-environment add_relation(environment const & env, name const & n, bool persistent) {
-    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Relation, n), persistent);
+environment add_relation(environment const & env, name const & n, name const & ns, bool persistent) {
+    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Relation, n), ns, persistent);
 }
 
-environment add_subst(environment const & env, name const & n, bool persistent) {
-    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Subst, n), persistent);
+environment add_subst(environment const & env, name const & n, name const & ns, bool persistent) {
+    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Subst, n), ns, persistent);
 }
 
-environment add_refl(environment const & env, name const & n, bool persistent) {
-    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Refl, n), persistent);
+environment add_refl(environment const & env, name const & n, name const & ns, bool persistent) {
+    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Refl, n), ns, persistent);
 }
 
-environment add_symm(environment const & env, name const & n, bool persistent) {
-    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Symm, n), persistent);
+environment add_symm(environment const & env, name const & n, name const & ns, bool persistent) {
+    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Symm, n), ns, persistent);
 }
 
-environment add_trans(environment const & env, name const & n, bool persistent) {
-    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Trans, n), persistent);
+environment add_trans(environment const & env, name const & n, name const & ns, bool persistent) {
+    return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Trans, n), ns, persistent);
 }
 
 static optional<relation_lemma_info> get_info(name_map<relation_lemma_info> const & table, name const & op) {
diff --git a/src/library/relation_manager.h b/src/library/relation_manager.h
index bd2d9be74..a3b421ce1 100644
--- a/src/library/relation_manager.h
+++ b/src/library/relation_manager.h
@@ -44,14 +44,14 @@ typedef std::function<bool(expr const &, name &, expr &, expr &)> is_relation_pr
 is_relation_pred mk_is_relation_pred(environment const & env);
 
 /** \brief Declare a new binary relation named \c n */
-environment add_relation(environment const & env, name const & n, bool persistent = true);
+environment add_relation(environment const & env, name const & n, name const & ns, bool persistent);
 
 /** \brief Declare subst/refl/symm/trans lemmas for a binary relation,
  * it also declares the relation if it has not been declared yet */
-environment add_subst(environment const & env, name const & n, bool persistent = true);
-environment add_refl(environment const & env, name const & n, bool persistent = true);
-environment add_symm(environment const & env, name const & n, bool persistent = true);
-environment add_trans(environment const & env, name const & n, bool persistent = true);
+environment add_subst(environment const & env, name const & n, name const & ns, bool persistent);
+environment add_refl(environment const & env, name const & n, name const & ns, bool persistent);
+environment add_symm(environment const & env, name const & n, name const & ns, bool persistent);
+environment add_trans(environment const & env, name const & n, name const & ns, bool persistent);
 
 struct relation_lemma_info {
     name     m_name;
diff --git a/src/library/scoped_ext.h b/src/library/scoped_ext.h
index 86c96f6e8..771e23f94 100644
--- a/src/library/scoped_ext.h
+++ b/src/library/scoped_ext.h
@@ -73,16 +73,13 @@ bool in_section(environment const & env);
          namespace bla
            namespace boo
               ...
-    Then, the procedure tries n, 'foo.bla.boo'+n, 'foo.bla'+n, 'foo'+n.
-*/
+    Then, the procedure tries n, 'foo.bla.boo'+n, 'foo.bla'+n, 'foo'+n. */
 optional<name> to_valid_namespace_name(environment const & env, name const & n);
 
 void open_scoped_ext(lua_State * L);
 
-/**
-   \brief Auxilary template used to simplify the creation of environment extensions that support
-   the scope
-*/
+/** \brief Auxilary template used to simplify the creation of environment extensions that support
+    the scope */
 template<typename Config>
 class scoped_ext : public environment_extension {
     typedef typename Config::state            state;
@@ -98,11 +95,19 @@ class scoped_ext : public environment_extension {
         return Config::get_fingerprint(e);
     }
 
+    /* Current state */
     state                 m_state;
+    /* Stack of states, it is updated using push/pop operations */
     list<state>           m_scopes;
-    list<list<entry>>     m_nonlocal_entries; // nonlocal entries per scope (for sections)
-    name_map<list<entry>> m_entries_map;      // namespace -> entries
+    /* Nonlocal entries per scope (for sections).
+       The nonlocal attributes declared in a section are not discarded when we close the section.
+       So, we keep a stack of the nonlocal entries associated with these attributes.
+       We re-add/declare them whenever a section is closed. */
+    list<list<entry>>     m_nonlocal_entries;
+    /* Mapping namespace -> entries for this namespace */
+    name_map<list<entry>> m_entries_map;
 
+    /* Update curret state with the entries from namespace \c n */
     void using_namespace_core(environment const & env, io_state const & ios, name const & n) {
         if (auto it = m_entries_map.find(n)) {
             buffer<entry> entries;
@@ -115,6 +120,7 @@ class scoped_ext : public environment_extension {
         }
     }
 
+    /* Add entry \c e to namespace \c n */
     void register_entry_core(name n, entry const & e) {
         if (auto it = m_entries_map.find(n))
             m_entries_map.insert(n, cons(e, *it));
@@ -122,10 +128,9 @@ class scoped_ext : public environment_extension {
             m_entries_map.insert(n, to_list(e));
     }
 
-    void add_entry_core(environment const & env, io_state const & ios, entry const & e) {
-        add_entry(env, ios, m_state, e);
-    }
-
+    /* Add entry \c e to namespace \c n. If \c n is the anonymous/root
+       namespace, then update current state with this entry.
+       This method is invoked when importing files. */
     scoped_ext _register_entry(environment const & env, io_state const & ios, name n, entry const & e) const {
         lean_assert(get_namespace(env).is_anonymous());
         scoped_ext r(*this);
@@ -135,6 +140,8 @@ class scoped_ext : public environment_extension {
         return r;
     }
 
+    /* Add a nonlocal entry. Register it in the current namespace, mark it as nonlocal, and
+       update current state */
     scoped_ext _add_entry(environment const & env, io_state const & ios, entry const & e) const {
         scoped_ext r(*this);
         r.register_entry_core(get_namespace(env), e);
@@ -144,32 +151,76 @@ class scoped_ext : public environment_extension {
         return r;
     }
 
+    /* Add entry to current state */
     scoped_ext _add_tmp_entry(environment const & env, io_state const & ios, entry const & e) const {
         scoped_ext r(*this);
         add_entry(env, ios, r.m_state, e);
         return r;
     }
 
+    /* Add \c e to the first \c n states in \c l.
+       \pre length(l) >= n */
+    static list<state> add_first_n(environment const & env, io_state const & ios, list<state> const & l, entry const & e, unsigned n) {
+        if (n == 0) {
+            return l;
+        } else {
+            state new_s = head(l);
+            add_entry(env, ios, new_s, e);
+            return cons(new_s, add_first_n(env, ios, tail(l), e, n-1));
+        }
+    }
+
+    scoped_ext _add_entry_at(environment const & env, io_state const & ios, entry const & e, name const & ns) const {
+        lean_assert(get_namespace(env) != ns);
+        scoped_ext r(*this);
+        r.register_entry_core(ns, e);
+        unsigned n     = 0;
+        bool     found = false;
+        lean_assert(length(m_scopes) == length(get_namespaces(env)));
+        if (ns.is_anonymous()) {
+            found = true;
+            n     = length(m_scopes);
+        } else {
+            for (name const & ns2 : get_namespaces(env)) {
+                if (ns == ns2) {
+                    found = true;
+                    break;
+                }
+                n++;
+            }
+        }
+        if (found) {
+            // must update m_nonlocal_entries
+            r.m_scopes = add_first_n(env, ios, r.m_scopes, e, n);
+            add_entry(env, ios, r.m_state, e);
+        }
+        return r;
+    }
+
 public:
+    /** \brief Return an updated state with the entries from namespace \c n. */
     scoped_ext using_namespace(environment const & env, io_state const & ios, name const & n) const {
         scoped_ext r(*this);
         r.using_namespace_core(env, ios, n);
         return r;
     }
 
-    environment export_namespace(environment env, io_state const & ios, name const & n) const {
-        if (auto it = m_entries_map.find(n)) {
+    /** \brief Copy entries from the given namespace to the current namespace. */
+    environment export_namespace(environment env, io_state const & ios, name const & ns) const {
+        if (auto it = m_entries_map.find(ns)) {
             buffer<entry> entries;
             to_buffer(*it, entries);
-            unsigned i = entries.size();
+            unsigned i      = entries.size();
+            name current_ns = get_namespace(env);
             while (i > 0) {
                 --i;
-                env = add_entry(env, ios, entries[i]);
+                env = add_entry(env, ios, entries[i], current_ns, true);
             }
         }
         return env;
     }
 
+    /** \brief Open a namespace/section. It return the new updated state. */
     scoped_ext push() const {
         scoped_ext r(*this);
         r.m_scopes           = cons(m_state, r.m_scopes);
@@ -177,6 +228,9 @@ public:
         return r;
     }
 
+    /** \brief Close namespace/section. It returns the new updated
+        state, and a list of entries that must be re-added/declared.
+        \pre There are open namespaces */
     pair<scoped_ext, list<entry>> pop(scope_kind k) const {
         lean_assert(!is_nil(m_scopes));
         scoped_ext r(*this);
@@ -234,24 +288,38 @@ public:
         }
         return new_env;
     }
+
     static environment register_entry(environment const & env, io_state const & ios, name const & n, entry const & e) {
         return update(env, get(env)._register_entry(env, ios, n, e));
     }
-    static environment add_entry(environment env, io_state const & ios, entry const & e, bool persistent = true) {
+
+    static environment add_entry(environment env, io_state const & ios, entry const & e, name const & n, bool persistent) {
         if (auto h = get_fingerprint(e)) {
             env = update_fingerprint(env, *h);
         }
-        if (!persistent) {
-            return update(env, get(env)._add_tmp_entry(env, ios, e));
+        if (n == get_namespace(env)) {
+            if (!persistent) {
+                return update(env, get(env)._add_tmp_entry(env, ios, e));
+            } else {
+                name n = get_namespace(env);
+                env = module::add(env, get_serialization_key(), [=](environment const &, serializer & s) {
+                        s << n;
+                        write_entry(s, e);
+                    });
+                return update(env, get(env)._add_entry(env, ios, e));
+            }
         } else {
-            name n = get_namespace(env);
+            lean_assert(!persistent);
+            // add entry in a namespace that is not the current one
             env = module::add(env, get_serialization_key(), [=](environment const &, serializer & s) {
                     s << n;
                     write_entry(s, e);
                 });
-            return update(env, get(env)._add_entry(env, ios, e));
+            env = add_namespace(env, n);
+            return update(env, get(env)._add_entry_at(env, ios, e, n));
         }
     }
+
     static void reader(deserializer & d, shared_environment &,
                        std::function<void(asynch_update_fn const &)> &,
                        std::function<void(delayed_update_fn const &)> & add_delayed_update) {
@@ -265,6 +333,7 @@ public:
     static state const & get_state(environment const & env) {
         return get(env).m_state;
     }
+    /** \brief Return the entries/attributes associated with the given namespace */
     static list<entry> const * get_entries(environment const & env, name const & n) {
         return get(env).m_entries_map.find(n);
     }
diff --git a/src/library/user_recursors.cpp b/src/library/user_recursors.cpp
index e2536c730..f6e5c847e 100644
--- a/src/library/user_recursors.cpp
+++ b/src/library/user_recursors.cpp
@@ -315,11 +315,11 @@ template class scoped_ext<recursor_config>;
 typedef scoped_ext<recursor_config> recursor_ext;
 
 environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos,
-                              bool persistent) {
+                              name const & ns, bool persistent) {
     if (inductive::is_elim_rule(env, r))
         throw exception(sstream() << "invalid user defined recursor, '" << r << "' is a builtin recursor");
     recursor_info info = mk_recursor_info(env, r, major_pos);
-    return recursor_ext::add_entry(env, get_dummy_ios(), info, persistent);
+    return recursor_ext::add_entry(env, get_dummy_ios(), info, ns, persistent);
 }
 
 recursor_info get_recursor_info(environment const & env, name const & r) {
diff --git a/src/library/user_recursors.h b/src/library/user_recursors.h
index d0e28b3d6..00224e48e 100644
--- a/src/library/user_recursors.h
+++ b/src/library/user_recursors.h
@@ -56,7 +56,7 @@ public:
     static recursor_info read(deserializer & d);
 };
 
-environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos, bool persistent);
+environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos, name const & ns, bool persistent);
 recursor_info get_recursor_info(environment const & env, name const & r);
 list<name> get_recursors_for(environment const & env, name const & I);
 bool is_user_defined_recursor(environment const & env, name const & r);
diff --git a/tests/lean/attr_at1.lean b/tests/lean/attr_at1.lean
new file mode 100644
index 000000000..da20ea472
--- /dev/null
+++ b/tests/lean/attr_at1.lean
@@ -0,0 +1,16 @@
+definition f (a : nat) := a + 1
+
+attribute f [reducible] at foo
+
+print f
+
+section
+  open foo
+  print f
+end
+
+print f
+
+namespace foo
+  print f
+end foo
diff --git a/tests/lean/attr_at1.lean.expected.out b/tests/lean/attr_at1.lean.expected.out
new file mode 100644
index 000000000..62ad7a2b7
--- /dev/null
+++ b/tests/lean/attr_at1.lean.expected.out
@@ -0,0 +1,8 @@
+definition f : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition f : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
diff --git a/tests/lean/attr_at2.lean b/tests/lean/attr_at2.lean
new file mode 100644
index 000000000..45b30add9
--- /dev/null
+++ b/tests/lean/attr_at2.lean
@@ -0,0 +1,26 @@
+namespace foo
+namespace bah
+namespace bla
+section
+section
+section
+
+definition f (a : nat) := a + 1
+attribute f [reducible] at foo.bah
+definition g (a : nat) := a + a
+attribute g [reducible] at _root_
+
+print "sec 3. " print f print g
+end
+print "sec 2. " print f print g
+end
+print "sec 1. " print f print g
+end
+print "foo.bah.bla. " print f print g
+end bla
+
+print "foo.bah. " print foo.bah.bla.f print foo.bah.bla.g
+end bah
+print "foo. " print foo.bah.bla.f print foo.bah.bla.g
+end foo
+print "root. " print foo.bah.bla.f print foo.bah.bla.g
diff --git a/tests/lean/attr_at2.lean.expected.out b/tests/lean/attr_at2.lean.expected.out
new file mode 100644
index 000000000..ecbee7757
--- /dev/null
+++ b/tests/lean/attr_at2.lean.expected.out
@@ -0,0 +1,35 @@
+sec 3. 
+definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+sec 2. 
+definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+sec 1. 
+definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+foo.bah.bla. 
+definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+foo.bah. 
+definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+foo. 
+definition foo.bah.bla.f : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a
+root. 
+definition foo.bah.bla.f : ℕ → ℕ :=
+λ (a : ℕ), a + 1
+definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
+λ (a : ℕ), a + a