diff --git a/src/emacs/lean-syntax.el b/src/emacs/lean-syntax.el
index 2c4e0ac7f..9c995213a 100644
--- a/src/emacs/lean-syntax.el
+++ b/src/emacs/lean-syntax.el
@@ -118,7 +118,7 @@
      (,(rx symbol-start "_" symbol-end) . 'font-lock-preprocessor-face)
      ;; modifiers
      (,(rx (or "\[persistent\]" "\[notation\]" "\[visible\]" "\[instance\]" "\[class\]" "\[parsing-only\]"
-               "\[coercion\]" "\[reducible\]" "\[irreducible\]" "\[semireducible\]" "\[quasireducible\]" "\[wf\]"
+               "\[coercion\]" "\[unfold-f\]" "\[reducible\]" "\[irreducible\]" "\[semireducible\]" "\[quasireducible\]" "\[wf\]"
                "\[whnf\]" "\[multiple-instances\]" "\[none\]"
                "\[decls\]" "\[declarations\]" "\[all-transparent\]" "\[coercions\]" "\[classes\]"
                "\[notations\]" "\[abbreviations\]" "\[begin-end-hints\]" "\[tactic-hints\]" "\[reduce-hints\]"))
diff --git a/src/frontends/lean/decl_cmds.cpp b/src/frontends/lean/decl_cmds.cpp
index 47c0adcef..3246096e3 100644
--- a/src/frontends/lean/decl_cmds.cpp
+++ b/src/frontends/lean/decl_cmds.cpp
@@ -300,6 +300,7 @@ struct decl_attributes {
     bool               m_is_class;
     bool               m_is_parsing_only;
     bool               m_has_multiple_instances;
+    bool               m_unfold_f_hint;
     optional<unsigned> m_priority;
     optional<unsigned> m_unfold_c_hint;
 
@@ -317,6 +318,7 @@ struct decl_attributes {
         m_is_class               = false;
         m_is_parsing_only        = false;
         m_has_multiple_instances = false;
+        m_unfold_f_hint          = false;
     }
 
     struct elim_choice_fn : public replace_visitor {
@@ -421,6 +423,9 @@ struct decl_attributes {
                                        "marked as '[parsing-only]'", pos);
                 m_is_parsing_only = true;
                 p.next();
+            } else if (p.curr_is_token(get_unfold_f_tk())) {
+                p.next();
+                m_unfold_f_hint = true;
             } else if (p.curr_is_token(get_unfold_c_tk())) {
                 p.next();
                 unsigned r = p.parse_small_nat();
@@ -469,7 +474,9 @@ struct decl_attributes {
             if (m_is_quasireducible)
                 env = set_reducible(env, d, reducible_status::Quasireducible, m_persistent);
             if (m_unfold_c_hint)
-                env = add_unfold_c_hint(env, d, m_unfold_c_hint, m_persistent);
+                env = add_unfold_c_hint(env, d, *m_unfold_c_hint, m_persistent);
+            if (m_unfold_f_hint)
+                env = add_unfold_f_hint(env, d, m_persistent);
         }
         if (m_is_class)
             env = add_class(env, d, m_persistent);
diff --git a/src/frontends/lean/token_table.cpp b/src/frontends/lean/token_table.cpp
index ff2559e8b..51f4a0e9c 100644
--- a/src/frontends/lean/token_table.cpp
+++ b/src/frontends/lean/token_table.cpp
@@ -93,7 +93,7 @@ void init_token_table(token_table & t) {
          "variables", "parameter", "parameters", "constant", "constants", "[persistent]", "[visible]", "[instance]",
          "[none]", "[class]", "[coercion]", "[reducible]", "[irreducible]", "[semireducible]", "[quasireducible]",
          "[parsing-only]", "[multiple-instances]",
-         "evaluate", "check", "eval", "[wf]", "[whnf]", "[all-transparent]", "[priority", "[unfold-c", "print",
+         "evaluate", "check", "eval", "[wf]", "[whnf]", "[all-transparent]", "[priority", "[unfold-f]", "[unfold-c", "print",
          "end", "namespace", "section", "prelude", "help",
          "import", "inductive", "record", "structure", "module", "universe", "universes", "local",
          "precedence", "reserve", "infixl", "infixr", "infix", "postfix", "prefix", "notation", "context",
diff --git a/src/frontends/lean/tokens.cpp b/src/frontends/lean/tokens.cpp
index 99a37f2e7..9b0a62995 100644
--- a/src/frontends/lean/tokens.cpp
+++ b/src/frontends/lean/tokens.cpp
@@ -102,6 +102,7 @@ static name * g_opaque       = nullptr;
 static name * g_instance     = nullptr;
 static name * g_priority     = nullptr;
 static name * g_unfold_c     = nullptr;
+static name * g_unfold_f     = nullptr;
 static name * g_coercion     = nullptr;
 static name * g_reducible    = nullptr;
 static name * g_quasireducible = nullptr;
@@ -227,6 +228,7 @@ void initialize_tokens() {
     g_instance     = new name("[instance]");
     g_priority     = new name("[priority");
     g_unfold_c     = new name("[unfold-c");
+    g_unfold_f     = new name("[unfold-f]");
     g_coercion     = new name("[coercion]");
     g_reducible    = new name("[reducible]");
     g_quasireducible = new name("[quasireducible]");
@@ -290,6 +292,7 @@ void finalize_tokens() {
     delete g_instance;
     delete g_priority;
     delete g_unfold_c;
+    delete g_unfold_f;
     delete g_coercion;
     delete g_reducible;
     delete g_quasireducible;
@@ -479,6 +482,7 @@ name const & get_opaque_tk() { return *g_opaque; }
 name const & get_instance_tk() { return *g_instance; }
 name const & get_priority_tk() { return *g_priority; }
 name const & get_unfold_c_tk() { return *g_unfold_c; }
+name const & get_unfold_f_tk() { return *g_unfold_f; }
 name const & get_coercion_tk() { return *g_coercion; }
 name const & get_reducible_tk() { return *g_reducible; }
 name const & get_quasireducible_tk() { return *g_quasireducible; }
diff --git a/src/frontends/lean/tokens.h b/src/frontends/lean/tokens.h
index cc7e0e8b1..4a1c1ab44 100644
--- a/src/frontends/lean/tokens.h
+++ b/src/frontends/lean/tokens.h
@@ -104,6 +104,7 @@ name const & get_opaque_tk();
 name const & get_instance_tk();
 name const & get_priority_tk();
 name const & get_unfold_c_tk();
+name const & get_unfold_f_tk();
 name const & get_coercion_tk();
 name const & get_reducible_tk();
 name const & get_semireducible_tk();
diff --git a/src/library/normalize.cpp b/src/library/normalize.cpp
index 3b13a41aa..a2f825d77 100644
--- a/src/library/normalize.cpp
+++ b/src/library/normalize.cpp
@@ -19,42 +19,64 @@ Author: Leonardo de Moura
 
 namespace lean {
 /**
-   \brief c_unfold hint instructs the normalizer (and simplifier) that
-   a function application (f a_1 ... a_i ... a_n) should be unfolded
-   when argument a_i is a constructor.
+   \brief unfold hints instruct the normalizer (and simplifier) that
+   a function application. We have two kinds of hints:
+   - unfold_c (f a_1 ... a_i ... a_n) should be unfolded
+     when argument a_i is a constructor.
+   - unfold_f (f a_1 ... a_i ... a_n) should be unfolded when it is fully applied.
 */
-struct unfold_c_hint_entry {
-    name               m_decl_name;
-    optional<unsigned> m_arg_idx;
-    unfold_c_hint_entry() {}
-    unfold_c_hint_entry(name const & n, optional<unsigned> const & idx):m_decl_name(n), m_arg_idx(idx) {}
+struct unfold_hint_entry {
+    bool     m_unfold_c; //!< true if it is an unfold_c hint
+    bool     m_add;      //!< add/remove hint
+    name     m_decl_name;
+    unsigned m_arg_idx;
+    unfold_hint_entry():m_unfold_c(false), m_add(false), m_arg_idx(0) {}
+    unfold_hint_entry(bool unfold_c, bool add, name const & n, unsigned idx):
+        m_unfold_c(unfold_c), m_add(add), m_decl_name(n), m_arg_idx(idx) {}
 };
 
-static name * g_unfold_c_hint_name = nullptr;
+unfold_hint_entry mk_add_unfold_c_entry(name const & n, unsigned idx) { return unfold_hint_entry(true, true, n, idx); }
+unfold_hint_entry mk_erase_unfold_c_entry(name const & n) { return unfold_hint_entry(true, false, n, 0); }
+unfold_hint_entry mk_add_unfold_f_entry(name const & n) { return unfold_hint_entry(false, true, n, 0); }
+unfold_hint_entry mk_erase_unfold_f_entry(name const & n) { return unfold_hint_entry(false, false, n, 0); }
+
+static name * g_unfold_hint_name = nullptr;
 static std::string * g_key = nullptr;
 
-struct unfold_c_hint_config {
-    typedef name_map<unsigned>  state;
-    typedef unfold_c_hint_entry entry;
+struct unfold_hint_state {
+    name_map<unsigned>  m_unfold_c;
+    name_set            m_unfold_f;
+};
+
+struct unfold_hint_config {
+    typedef unfold_hint_state state;
+    typedef unfold_hint_entry entry;
 
     static void add_entry(environment const &, io_state const &, state & s, entry const & e) {
-        if (e.m_arg_idx)
-            s.insert(e.m_decl_name, *e.m_arg_idx);
-        else
-            s.erase(e.m_decl_name);
+        if (e.m_unfold_c) {
+            if (e.m_add)
+                s.m_unfold_c.insert(e.m_decl_name, e.m_arg_idx);
+            else
+                s.m_unfold_c.erase(e.m_decl_name);
+        } else {
+            if (e.m_add)
+                s.m_unfold_f.insert(e.m_decl_name);
+            else
+                s.m_unfold_f.erase(e.m_decl_name);
+        }
     }
     static name const & get_class_name() {
-        return *g_unfold_c_hint_name;
+        return *g_unfold_hint_name;
     }
     static std::string const & get_serialization_key() {
         return *g_key;
     }
     static void  write_entry(serializer & s, entry const & e) {
-        s << e.m_decl_name << e.m_arg_idx;
+        s << e.m_unfold_c << e.m_add << e.m_decl_name << e.m_arg_idx;
     }
     static entry read_entry(deserializer & d) {
         entry e;
-        d >> e.m_decl_name >> e.m_arg_idx;
+        d >> e.m_unfold_c >> e.m_add >> e.m_decl_name >> e.m_arg_idx;
         return e;
     }
     static optional<unsigned> get_fingerprint(entry const & e) {
@@ -62,33 +84,53 @@ struct unfold_c_hint_config {
     }
 };
 
-template class scoped_ext<unfold_c_hint_config>;
-typedef scoped_ext<unfold_c_hint_config> unfold_c_hint_ext;
+template class scoped_ext<unfold_hint_config>;
+typedef scoped_ext<unfold_hint_config> unfold_hint_ext;
 
-environment add_unfold_c_hint(environment const & env, name const & n, optional<unsigned> idx, bool persistent) {
+environment add_unfold_c_hint(environment const & env, name const & n, unsigned idx, bool persistent) {
     declaration const & d = env.get(n);
     if (!d.is_definition() || d.is_opaque())
         throw exception("invalid unfold-c hint, declaration must be a non-opaque definition");
-    return unfold_c_hint_ext::add_entry(env, get_dummy_ios(), unfold_c_hint_entry(n, idx), persistent);
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_c_entry(n, idx), persistent);
 }
 
 optional<unsigned> has_unfold_c_hint(environment const & env, name const & d) {
-    name_map<unsigned> const & s = unfold_c_hint_ext::get_state(env);
-    if (auto it = s.find(d))
+    unfold_hint_state const & s = unfold_hint_ext::get_state(env);
+    if (auto it = s.m_unfold_c.find(d))
         return optional<unsigned>(*it);
     else
         return optional<unsigned>();
 }
 
+environment erase_unfold_c_hint(environment const & env, name const & n, bool persistent) {
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_c_entry(n), persistent);
+}
+
+environment add_unfold_f_hint(environment const & env, name const & n, bool persistent) {
+    declaration const & d = env.get(n);
+    if (!d.is_definition() || d.is_opaque())
+        throw exception("invalid unfold-f hint, declaration must be a non-opaque definition");
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_add_unfold_f_entry(n), persistent);
+}
+
+bool has_unfold_f_hint(environment const & env, name const & d) {
+    unfold_hint_state const & s = unfold_hint_ext::get_state(env);
+    return s.m_unfold_f.contains(d);
+}
+
+environment erase_unfold_f_hint(environment const & env, name const & n, bool persistent) {
+    return unfold_hint_ext::add_entry(env, get_dummy_ios(), mk_erase_unfold_f_entry(n), persistent);
+}
+
 void initialize_normalize() {
-    g_unfold_c_hint_name = new name("c-unfold");
-    g_key = new std::string("c-unfold");
-    unfold_c_hint_ext::initialize();
+    g_unfold_hint_name = new name("unfold-hints");
+    g_key = new std::string("unfoldh");
+    unfold_hint_ext::initialize();
 }
 
 void finalize_normalize() {
-    unfold_c_hint_ext::finalize();
-    delete g_unfold_c_hint_name;
+    unfold_hint_ext::finalize();
+    delete g_unfold_hint_name;
     delete g_key;
 }
 
@@ -113,6 +155,10 @@ class normalize_fn {
         return ::lean::has_unfold_c_hint(m_tc.env(), const_name(f));
     }
 
+    bool has_unfold_f_hint(expr const & f) {
+        return is_constant(f) &&  ::lean::has_unfold_f_hint(m_tc.env(), const_name(f));
+    }
+
     expr normalize_app(expr const & e) {
         buffer<expr> args;
         bool modified = false;
@@ -123,6 +169,12 @@ class normalize_fn {
                 modified = true;
             a = new_a;
         }
+        if (has_unfold_f_hint(f)) {
+            if (!is_pi(m_tc.whnf(m_tc.infer(e).first).first)) {
+                if (optional<expr> r = unfold_app(m_tc.env(), mk_rev_app(f, args)))
+                    return normalize(*r);
+            }
+        }
         if (auto idx = has_unfold_c_hint(f)) {
             if (*idx < args.size() && is_constructor_app(m_tc.env(), args[args.size() - *idx - 1])) {
                 if (optional<expr> r = unfold_app(m_tc.env(), mk_rev_app(f, args)))
diff --git a/src/library/normalize.h b/src/library/normalize.h
index 216163943..7da2a0afa 100644
--- a/src/library/normalize.h
+++ b/src/library/normalize.h
@@ -32,27 +32,26 @@ expr normalize(type_checker & tc, expr const & e, constraint_seq & cs, bool eta
 expr normalize(type_checker & tc, expr const & e, std::function<bool(expr const&)> const & pred, // NOLINT
                constraint_seq & cs, bool eta = false);
 
-/** \brief c_unfold hint instructs the normalizer (and simplifier) that
+/** \brief unfold-c hint instructs the normalizer (and simplifier) that
     a function application (f a_1 ... a_i ... a_n) should be unfolded
     when argument a_i is a constructor.
 
     The constant will be unfolded even if it the whnf procedure did not unfolded it.
 
     Of course, kernel opaque constants are not unfolded.
-
-    \remark If idx is none, then the hint is removed.
 */
-environment add_unfold_c_hint(environment const & env, name const & n, optional<unsigned> idx, bool persistent = true);
-inline environment add_unfold_c_hint(environment const & env, name const & n, unsigned idx, bool persistent = true) {
-    return add_unfold_c_hint(env, n, optional<unsigned>(idx), persistent);
-}
-inline environment erase_unfold_c_hint(environment const & env, name const & n, bool persistent = true) {
-    return add_unfold_c_hint(env, n, optional<unsigned>(), persistent);
-}
-
+environment add_unfold_c_hint(environment const & env, name const & n, unsigned idx, bool persistent = true);
+environment erase_unfold_c_hint(environment const & env, name const & n, bool persistent = true);
 /** \brief Retrieve the hint added with the procedure add_unfold_c_hint. */
 optional<unsigned> has_unfold_c_hint(environment const & env, name const & d);
 
+/** \brief unfold-f hint instructs normalizer (and simplifier) that function application
+    (f a_1 ... a_n) should be unfolded when it is fully applied */
+environment add_unfold_f_hint(environment const & env, name const & n, bool persistent = true);
+environment erase_unfold_f_hint(environment const & env, name const & n, bool persistent = true);
+/** \brief Retrieve the hint added with the procedure add_unfold_f_hint. */
+optional<unsigned> has_unfold_f_hint(environment const & env, name const & d);
+
 void initialize_normalize();
 void finalize_normalize();
 }
diff --git a/tests/lean/unfoldf.lean b/tests/lean/unfoldf.lean
new file mode 100644
index 000000000..8deb1c48c
--- /dev/null
+++ b/tests/lean/unfoldf.lean
@@ -0,0 +1,28 @@
+open nat
+
+definition id [unfold-f] {A : Type} (a : A) := a
+definition compose {A B C : Type} (g : B → C) (f : A → B) (a : A) := g (f a)
+notation g ∘ f := compose g f
+
+example (a b : nat) (H : a = b) : id a = b :=
+begin
+  esimp,
+  state,
+  exact H
+end
+
+example (a b : nat) (H : a = b) : (id ∘ id) a = b :=
+begin
+  esimp,
+  state,
+  exact H
+end
+
+attribute compose [unfold-f]
+
+example (a b : nat) (H : a = b) : (id ∘ id) a = b :=
+begin
+  esimp,
+  state,
+  exact H
+end
diff --git a/tests/lean/unfoldf.lean.expected.out b/tests/lean/unfoldf.lean.expected.out
new file mode 100644
index 000000000..68e8113e0
--- /dev/null
+++ b/tests/lean/unfoldf.lean.expected.out
@@ -0,0 +1,12 @@
+unfoldf.lean:10:2: proof state
+a b : ℕ,
+H : a = b
+⊢ a = b
+unfoldf.lean:17:2: proof state
+a b : ℕ,
+H : a = b
+⊢ (id ∘ id) a = b
+unfoldf.lean:26:2: proof state
+a b : ℕ,
+H : a = b
+⊢ a = b