diff --git a/src/frontends/lean/frontend.cpp b/src/frontends/lean/frontend.cpp
index e65645bc8..61e03b661 100644
--- a/src/frontends/lean/frontend.cpp
+++ b/src/frontends/lean/frontend.cpp
@@ -241,7 +241,7 @@ struct frontend::imp {
         if (has_children())
             throw exception(sstream() << "failed to mark implicit arguments, frontend object is read-only");
         object const & obj = m_env.get_object(n);
-        if (obj.kind() != object_kind::Definition && obj.kind() != object_kind::Postulate)
+        if (obj.kind() != object_kind::Definition && obj.kind() != object_kind::Postulate && obj.kind() != object_kind::Builtin)
             throw exception(sstream() << "failed to mark implicit arguments, the object '" << n << "' is not a definition or postulate");
         if (has_implicit_arguments(n))
             throw exception(sstream() << "the object '" << n << "' already has implicit argument information associated with it");
@@ -425,6 +425,14 @@ operator_info frontend::find_led(name const & n) const { return m_ptr->find_led(
 
 void frontend::mark_implicit_arguments(name const & n, unsigned sz, bool const * implicit) { m_ptr->mark_implicit_arguments(n, sz, implicit); }
 void frontend::mark_implicit_arguments(name const & n, std::initializer_list<bool> const & l) { mark_implicit_arguments(n, l.size(), l.begin()); }
+void frontend::mark_implicit_arguments(expr const & n, std::initializer_list<bool> const & l) {
+    if (is_constant(n)) {
+        mark_implicit_arguments(const_name(n), l);
+    } else {
+        lean_assert(is_value(n));
+        mark_implicit_arguments(to_value(n).get_name(), l);
+    }
+}
 bool frontend::has_implicit_arguments(name const & n) const { return m_ptr->has_implicit_arguments(n); }
 std::vector<bool> const & frontend::get_implicit_arguments(name const & n) const { return m_ptr->get_implicit_arguments(n); }
 name const & frontend::get_explicit_version(name const & n) const { return m_ptr->get_explicit_version(n); }
diff --git a/src/frontends/lean/frontend.h b/src/frontends/lean/frontend.h
index 9def83427..68a5b0e42 100644
--- a/src/frontends/lean/frontend.h
+++ b/src/frontends/lean/frontend.h
@@ -135,7 +135,7 @@ public:
     */
     void mark_implicit_arguments(name const & n, unsigned sz, bool const * mask);
     void mark_implicit_arguments(name const & n, std::initializer_list<bool> const & l);
-    void mark_implicit_arguments(expr const & n, std::initializer_list<bool> const & l) { mark_implicit_arguments(const_name(n), l); }
+    void mark_implicit_arguments(expr const & n, std::initializer_list<bool> const & l);
     /** \brief Return true iff \c n has implicit arguments */
     bool has_implicit_arguments(name const & n) const;
     /** \brief Return the position of the arguments that are implicit. */
diff --git a/src/frontends/lean/notation.cpp b/src/frontends/lean/notation.cpp
index 00c8a5032..0b8fbb738 100644
--- a/src/frontends/lean/notation.cpp
+++ b/src/frontends/lean/notation.cpp
@@ -16,6 +16,7 @@ namespace lean {
 */
 void init_builtin_notation(frontend & f) {
     f.mark_implicit_arguments(mk_homo_eq_fn(), {true, false, false});
+    f.mark_implicit_arguments(mk_if_fn(), {true, false, false, false});
     f.add_infix("==", 50, mk_homo_eq_fn());
     f.add_infix("≃",  50, mk_homo_eq_fn());
 
diff --git a/src/frontends/lean/parser.cpp b/src/frontends/lean/parser.cpp
index c9d81b484..40a7c4ad4 100644
--- a/src/frontends/lean/parser.cpp
+++ b/src/frontends/lean/parser.cpp
@@ -545,12 +545,13 @@ class parser::imp {
         object const & obj = m_frontend.find_object(id);
         if (obj) {
             object_kind k      = obj.kind();
-            if (k == object_kind::Definition || k == object_kind::Postulate) {
+            if (k == object_kind::Definition || k == object_kind::Postulate || k == object_kind::Builtin) {
                 if (m_frontend.has_implicit_arguments(obj.get_name())) {
                     std::vector<bool> const & imp_args = m_frontend.get_implicit_arguments(obj.get_name());
                     buffer<expr> args;
                     pos_info p = pos();
-                    args.push_back(save(mk_constant(obj.get_name()), p));
+                    expr f = (k == object_kind::Builtin) ? obj.get_value() : mk_constant(obj.get_name());
+                    args.push_back(save(f, p));
                     // We parse all the arguments to make sure we
                     // get all explicit arguments.
                     for (unsigned i = 0; i < imp_args.size(); i++) {
@@ -561,11 +562,11 @@ class parser::imp {
                         }
                     }
                     return mk_app(args);
+                } else if (k == object_kind::Builtin) {
+                    return obj.get_value();
                 } else {
                     return mk_constant(obj.get_name());
                 }
-            } else if (k == object_kind::Builtin) {
-                return obj.get_value();
             } else {
                 throw parser_error(sstream() << "invalid object reference, object '" << id << "' is not an expression.", p);
             }
diff --git a/src/frontends/lean/pp.cpp b/src/frontends/lean/pp.cpp
index 134c56724..f6a7b0da1 100644
--- a/src/frontends/lean/pp.cpp
+++ b/src/frontends/lean/pp.cpp
@@ -244,7 +244,12 @@ class pp_fn {
     }
 
     result pp_value(expr const & e) {
-        return mk_result(to_value(e).pp(m_unicode), 1);
+        value const & v = to_value(e);
+        if (has_implicit_arguments(v.get_name())) {
+            return mk_result(format(m_frontend.get_explicit_version(v.get_name())), 1);
+        } else {
+            return mk_result(v.pp(m_unicode), 1);
+        }
     }
 
     result pp_type(expr const & e) {
@@ -506,18 +511,25 @@ class pp_fn {
         std::vector<bool> const * m_implicit_args;
         bool         m_notation_enabled;
 
+        static bool has_implicit_arguments(pp_fn const & owner, expr const & f) {
+            return
+                (is_constant(f) && owner.has_implicit_arguments(const_name(f))) ||
+                (is_value(f)    && owner.has_implicit_arguments(to_value(f).get_name()));
+        }
+
         application(expr const & e, pp_fn const & owner, bool show_implicit):m_app(e) {
             frontend const & fe = owner.m_frontend;
             expr const & f = arg(e, 0);
-            if (is_constant(f) && owner.has_implicit_arguments(const_name(f))) {
-                m_implicit_args = &(fe.get_implicit_arguments(const_name(f)));
+            if (has_implicit_arguments(owner, f)) {
+                name const & n = is_constant(f) ? const_name(f) : to_value(f).get_name();
+                m_implicit_args = &(fe.get_implicit_arguments(n));
                 if (show_implicit || num_args(e) - 1 < m_implicit_args->size()) {
                     // we are showing implicit arguments, thus we do
                     // not need the bit-mask for implicit arguments
                     m_implicit_args = nullptr;
                     // we use the explicit name of f, to make it clear
                     // that we are exposing implicit arguments
-                    m_f = mk_constant(fe.get_explicit_version(const_name(f)));
+                    m_f = mk_constant(fe.get_explicit_version(n));
                     m_notation_enabled = false;
                 } else {
                     m_f = f;
@@ -683,7 +695,13 @@ class pp_fn {
         } else {
             // standard function application
             expr const & f  = app.get_function();
-            result p        = is_constant(f) ? mk_result(format(const_name(f)), 1) : pp_child(f, depth);
+            result p;
+            if (is_constant(f))
+                p = mk_result(format(const_name(f)), 1);
+            else if (is_value(f))
+                p = mk_result(to_value(f).pp(m_unicode), 1);
+            else
+                p = pp_child(f, depth);
             bool simple     = is_constant(f) && const_name(f).size() <= m_indent + 4;
             unsigned indent = simple ? const_name(f).size()+1 : m_indent;
             format   r_format = p.first;
diff --git a/tests/lean/arith7.lean.expected.out b/tests/lean/arith7.lean.expected.out
index 7f88d3d8d..deeb4397c 100644
--- a/tests/lean/arith7.lean.expected.out
+++ b/tests/lean/arith7.lean.expected.out
@@ -6,7 +6,7 @@
 2
 ⊤
   Assumed: y
-if ℤ (0 ≤ -3 + y) (-3 + y) (-1 * (-3 + y))
+if (0 ≤ -3 + y) (-3 + y) (-1 * (-3 + y))
 | x + y | > x
   Set: lean::pp::notation
 Int::gt (Int::abs (Int::add x y)) x
diff --git a/tests/lean/elab1.lean.expected.out b/tests/lean/elab1.lean.expected.out
index 0ced617cf..539db6df8 100644
--- a/tests/lean/elab1.lean.expected.out
+++ b/tests/lean/elab1.lean.expected.out
@@ -553,7 +553,7 @@ Failed to solve
                  ⊢ ?M3::1 ≈ Type U
                     Assumption 29
 Failed to solve
-a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≺ if Bool (if Bool a b ⊤) a ⊤
+a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≺ if (if a b ⊤) a ⊤
     Substitution
     a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≺ ?M3::5[lift:0:1]
         Substitution
@@ -572,29 +572,29 @@ a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≺ if Bool (if Bool a b ⊤
             Assignment
             a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≈ ?M3::8
                 Destruct/Decompose
-                a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if Bool a b ⊤ ≈ if Bool ?M3::8 ?M3::9 ⊤
+                a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if a b ⊤ ≈ if ?M3::8 ?M3::9 ⊤
                     Normalize
-                    a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if Bool a b ⊤ ≈ ?M3::8 ⇒ ?M3::9
+                    a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if a b ⊤ ≈ ?M3::8 ⇒ ?M3::9
                         Substitution
-                        a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if Bool a b ⊤ ≈ ?M3::10
+                        a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ if a b ⊤ ≈ ?M3::10
                             Destruct/Decompose
                             a : Bool,
                             b : Bool,
                             H : ?M3::2,
                             H_na : ?M3::7 ⊢
-                            if Bool (if Bool a b ⊤) a ⊤ ≺ if Bool ?M3::10 ?M3::11 ⊤
+                            if (if a b ⊤) a ⊤ ≺ if ?M3::10 ?M3::11 ⊤
                                 Normalize
                                 a : Bool,
                                 b : Bool,
                                 H : ?M3::2,
                                 H_na : ?M3::7 ⊢
-                                (a ⇒ b) ⇒ a ≺ if Bool ?M3::10 ?M3::11 ⊤
+                                (a ⇒ b) ⇒ a ≺ if ?M3::10 ?M3::11 ⊤
                                     Substitution
                                     a : Bool,
                                     b : Bool,
                                     H : ?M3::2,
                                     H_na : ?M3::7 ⊢
-                                    ?M3::2[lift:0:2] ≺ if Bool ?M3::10 ?M3::11 ⊤
+                                    ?M3::2[lift:0:2] ≺ if ?M3::10 ?M3::11 ⊤
                                         Normalize
                                         a : Bool,
                                         b : Bool,
@@ -650,7 +650,7 @@ a : Bool, b : Bool, H : ?M3::2, H_na : ?M3::7 ⊢ a ≺ if Bool (if Bool a b ⊤
                                         ?M3::9
                                         MT H H_na
         Assignment
-        a : Bool, b : Bool, H : ?M3::2 ⊢ if Bool (if Bool a b ⊤) a ⊤ ≺ ?M3::5
+        a : Bool, b : Bool, H : ?M3::2 ⊢ if (if a b ⊤) a ⊤ ≺ ?M3::5
             Normalize
             a : Bool, b : Bool, H : ?M3::2 ⊢ (a ⇒ b) ⇒ a ≺ ?M3::5
                 Normalize
diff --git a/tests/lean/ho.lean.expected.out b/tests/lean/ho.lean.expected.out
index bb69c70ad..324be8ef8 100644
--- a/tests/lean/ho.lean.expected.out
+++ b/tests/lean/ho.lean.expected.out
@@ -7,4 +7,4 @@
   Assumed: H2
   Proved: T1
 Axiom H2 : (g a) > 0
-Theorem T1 : (g b) > 0 := Subst (λ x : ℤ, if Bool ((g x) ≤ 0) ⊥ ⊤) H2 H1
+Theorem T1 : (g b) > 0 := Subst (λ x : ℤ, if ((g x) ≤ 0) ⊥ ⊤) H2 H1
diff --git a/tests/lean/tst1.lean b/tests/lean/tst1.lean
index 28a8455e5..498b709bb 100644
--- a/tests/lean/tst1.lean
+++ b/tests/lean/tst1.lean
@@ -9,7 +9,7 @@ Infix 50 < : lt
 Axiom two_lt_three : two < three
 Definition vector (A : Type) (n : N) : Type := Pi (i : N) (H : i < n), A
 Definition const {A : Type} (n : N) (d : A) : vector A n := fun (i : N) (H : i < n), d
-Definition update {A : Type} {n : N} (v : vector A n) (i : N) (d : A) : vector A n := fun (j : N) (H : j < n), if A (j = i) d (v j H)
+Definition update {A : Type} {n : N} (v : vector A n) (i : N) (d : A) : vector A n := fun (j : N) (H : j < n), if (j = i) d (v j H)
 Definition select {A : Type} {n : N} (v : vector A n) (i : N) (H : i < n) : A := v i H
 Definition map {A B C : Type} {n : N} (f : A -> B -> C) (v1 : vector A n) (v2 : vector B n) : vector C n := fun (i : N) (H : i < n), f (v1 i H) (v2 i H)
 Show Environment 10
diff --git a/tests/lean/tst1.lean.expected.out b/tests/lean/tst1.lean.expected.out
index 1d2b09ca0..ff9a7e0a6 100644
--- a/tests/lean/tst1.lean.expected.out
+++ b/tests/lean/tst1.lean.expected.out
@@ -17,7 +17,7 @@ Definition vector (A : Type) (n : N) : Type := Π (i : N), (i < n) → A
 Definition const {A : Type} (n : N) (d : A) : vector A n := λ (i : N) (H : i < n), d
 Definition const::explicit (A : Type) (n : N) (d : A) : vector A n := const n d
 Definition update {A : Type} {n : N} (v : vector A n) (i : N) (d : A) : vector A n :=
-    λ (j : N) (H : j < n), if A (j = i) d (v j H)
+    λ (j : N) (H : j < n), if (j = i) d (v j H)
 Definition update::explicit (A : Type) (n : N) (v : vector A n) (i : N) (d : A) : vector A n := update v i d
 Definition select {A : Type} {n : N} (v : vector A n) (i : N) (H : i < n) : A := v i H
 Definition select::explicit (A : Type) (n : N) (v : vector A n) (i : N) (H : i < n) : A := select v i H
@@ -26,7 +26,7 @@ Definition map {A B C : Type} {n : N} (f : A → B → C) (v1 : vector A n) (v2
 Definition map::explicit (A B C : Type) (n : N) (f : A → B → C) (v1 : vector A n) (v2 : vector B n) : vector C n :=
     map f v1 v2
 select (update (const three ⊥) two ⊤) two two_lt_three : Bool
-if Bool (two = two) ⊤ ⊥
+if (two = two) ⊤ ⊥
 update (const three ⊥) two ⊤ : vector Bool three
 
 --------
@@ -46,4 +46,4 @@ map normal form -->
   f (v1 i H) (v2 i H)
 
 update normal form --> 
-λ (A : Type) (n : N) (v : Π (i : N), (i < n) → A) (i : N) (d : A) (j : N) (H : j < n), if A (j = i) d (v j H)
+λ (A : Type) (n : N) (v : Π (i : N), (i < n) → A) (i : N) (d : A) (j : N) (H : j < n), if (j = i) d (v j H)
diff --git a/tests/lean/tst10.lean.expected.out b/tests/lean/tst10.lean.expected.out
index 1662bf192..5a3d50686 100644
--- a/tests/lean/tst10.lean.expected.out
+++ b/tests/lean/tst10.lean.expected.out
@@ -15,7 +15,7 @@ a ∨ b
 a ∨ a ∨ b
 a ⇒ b ⇒ a
 a ⇒ b : Bool
-if Bool a a ⊤
+if a a ⊤
 a
   Assumed: H1
   Assumed: H2
diff --git a/tests/lean/tst17.lean.expected.out b/tests/lean/tst17.lean.expected.out
index da9a2e901..8238bde24 100644
--- a/tests/lean/tst17.lean.expected.out
+++ b/tests/lean/tst17.lean.expected.out
@@ -5,6 +5,5 @@
 ∀ a b : Type, ∃ c : Type, (g a b) = (f c)
 ∀ a b : Type, ∃ c : Type, (g a b) = (f c) : Bool
 (λ a : Type,
-   (λ b : Type, if Bool ((λ x : Type, if Bool ((g a b) = (f x)) ⊥ ⊤) = (λ x : Type, ⊤)) ⊥ ⊤) =
-   (λ x : Type, ⊤)) =
+   (λ b : Type, if ((λ x : Type, if ((g a b) = (f x)) ⊥ ⊤) = (λ x : Type, ⊤)) ⊥ ⊤) = (λ x : Type, ⊤)) =
 (λ x : Type, ⊤)