diff --git a/src/frontends/lean/notation_cmd.cpp b/src/frontends/lean/notation_cmd.cpp
index b9778a3c8..4ab8f1b89 100644
--- a/src/frontends/lean/notation_cmd.cpp
+++ b/src/frontends/lean/notation_cmd.cpp
@@ -309,7 +309,9 @@ static action parse_action(parser & p, name const & prev_token, unsigned default
                     locals.pop_back();
                     locals.pop_back();
                 }
-                expr ini  = parse_notation_expr(p, locals);
+                optional<expr> ini;
+                if (!p.curr_is_token(get_rparen_tk()) && !p.curr_is_quoted_symbol())
+                    ini = parse_notation_expr(p, locals);
                 optional<name> terminator;
                 if (!p.curr_is_token(get_rparen_tk()))
                     terminator = parse_quoted_symbol_or_token(p, new_tokens);
diff --git a/src/frontends/lean/parse_table.cpp b/src/frontends/lean/parse_table.cpp
index 317196591..ebc50b4b0 100644
--- a/src/frontends/lean/parse_table.cpp
+++ b/src/frontends/lean/parse_table.cpp
@@ -83,10 +83,10 @@ struct expr_action_cell : public action_cell {
 struct exprs_action_cell : public expr_action_cell {
     name           m_token_sep;
     expr           m_rec;
-    expr           m_ini;
+    optional<expr> m_ini;
     optional<name> m_terminator;
     bool           m_fold_right;
-    exprs_action_cell(name const & sep, expr const & rec, expr const & ini,
+    exprs_action_cell(name const & sep, expr const & rec, optional<expr> const & ini,
                       optional<name> const & terminator, bool right, unsigned rbp):
         expr_action_cell(action_kind::Exprs, rbp),
         m_token_sep(sep), m_rec(rec), m_ini(ini), m_terminator(terminator), m_fold_right(right) {}
@@ -151,7 +151,7 @@ expr const & action::get_rec() const {
         return to_exprs_action(m_ptr)->m_rec;
 }
 bool action::use_lambda_abstraction() const { return to_scoped_expr_action(m_ptr)->m_lambda; }
-expr const & action::get_initial() const { return to_exprs_action(m_ptr)->m_ini; }
+optional<expr> const & action::get_initial() const { return to_exprs_action(m_ptr)->m_ini; }
 bool action::is_fold_right() const { return to_exprs_action(m_ptr)->m_fold_right; }
 parse_fn const & action::get_parse_fn() const { return to_ext_action(m_ptr)->m_parse_fn; }
 std::string const & action::get_lua_fn() const { return to_ext_lua_action(m_ptr)->m_lua_fn; }
@@ -193,7 +193,9 @@ void action::display(std::ostream & out) const {
         out << "(fold" << (is_fold_right() ? "r" : "l");
         if (get_terminator())
             out << "*";
-        out << " " << rbp() << " " << get_rec() << " " << get_initial();
+        out << " " << rbp() << " " << get_rec();
+        if (get_initial())
+            out << " " << *get_initial();
         if (get_terminator())
             out << *get_terminator();
         out << ")";
@@ -239,13 +241,13 @@ void finalize_parse_table() {
 }
 
 action mk_expr_action(unsigned rbp) { return action(new expr_action_cell(rbp)); }
-action mk_exprs_action(name const & sep, expr const & rec, expr const & ini,
+action mk_exprs_action(name const & sep, expr const & rec, optional<expr> const & ini,
                        optional<name> const & terminator, bool right, unsigned rbp) {
     if (get_free_var_range(rec) > 2)
         throw exception("invalid notation, the expression used to combine a sequence of expressions "
                         "must not contain free variables with de Bruijn indices greater than 1");
     expr new_rec = annotate_macro_subterms(rec);
-    expr new_ini = annotate_macro_subterms(ini);
+    optional<expr> new_ini = ini ? some_expr(annotate_macro_subterms(*ini)) : none_expr();
     return action(new exprs_action_cell(sep, new_rec, new_ini, terminator, right, rbp));
 }
 action mk_scoped_expr_action(expr const & rec, unsigned rb, bool lambda) {
@@ -269,7 +271,7 @@ action replace(action const & a, std::function<expr(expr const &)> const & f) {
     case action_kind::Ext:  case action_kind::LuaExt: case action_kind::Expr:
         return a;
     case action_kind::Exprs:
-        return mk_exprs_action(a.get_sep(), f(a.get_rec()), f(a.get_initial()), a.get_terminator(),
+        return mk_exprs_action(a.get_sep(), f(a.get_rec()), a.get_initial() ? some_expr(f(*a.get_initial())) : none_expr(), a.get_terminator(),
                                a.is_fold_right(), a.rbp());
     case action_kind::ScopedExpr:
         return mk_scoped_expr_action(f(a.get_rec()), a.rbp(), a.use_lambda_abstraction());
@@ -498,7 +500,7 @@ static int mk_exprs_action(lua_State * L) {
     if (nargs >= 4) terminator = to_optional_name(L, 4);
     return push_notation_action(L, mk_exprs_action(to_name_ext(L, 1),
                                                    to_expr(L, 2),
-                                                   to_expr(L, 3),
+                                                   lua_isnil(L, 3) ? none_expr() : some_expr(to_expr(L, 3)),
                                                    terminator,
                                                    lua_toboolean(L, 5),
                                                    rbp));
@@ -540,7 +542,7 @@ static int rec(lua_State * L) {
 }
 static int initial(lua_State * L) {
     check_action(L, 1, { action_kind::Exprs });
-    return push_expr(L, to_notation_action(L, 1).get_initial());
+    return push_optional_expr(L, to_notation_action(L, 1).get_initial());
 }
 static int is_fold_right(lua_State * L) {
     check_action(L, 1, { action_kind::Exprs });
diff --git a/src/frontends/lean/parse_table.h b/src/frontends/lean/parse_table.h
index ffe210dd7..5ca90ae94 100644
--- a/src/frontends/lean/parse_table.h
+++ b/src/frontends/lean/parse_table.h
@@ -60,7 +60,7 @@ public:
 
     friend void initialize_parse_table();
     friend action mk_expr_action(unsigned rbp);
-    friend action mk_exprs_action(name const & sep, expr const & rec, expr const & ini,
+    friend action mk_exprs_action(name const & sep, expr const & rec, optional<expr> const & ini,
                                   optional<name> const & terminator, bool right, unsigned rbp);
     friend action mk_scoped_expr_action(expr const & rec, unsigned rbp, bool lambda);
     friend action mk_ext_action_core(parse_fn const & fn);
@@ -71,7 +71,7 @@ public:
     unsigned rbp() const;
     name const & get_sep() const;
     expr const & get_rec() const;
-    expr const & get_initial() const;
+    optional<expr> const & get_initial() const;
     optional<name> const & get_terminator() const;
     bool is_fold_right() const;
     bool use_lambda_abstraction() const;
@@ -89,7 +89,7 @@ inline bool operator!=(action const & a1, action const & a2) { return !a1.is_equ
 
 action mk_skip_action();
 action mk_expr_action(unsigned rbp = 0);
-action mk_exprs_action(name const & sep, expr const & rec, expr const & ini, optional<name> const & terminator, bool right,
+action mk_exprs_action(name const & sep, expr const & rec, optional<expr> const & ini, optional<name> const & terminator, bool right,
                        unsigned rbp = 0);
 action mk_binder_action();
 action mk_binders_action();
diff --git a/src/frontends/lean/parser.cpp b/src/frontends/lean/parser.cpp
index 6074c73d1..406a83eb4 100644
--- a/src/frontends/lean/parser.cpp
+++ b/src/frontends/lean/parser.cpp
@@ -903,9 +903,15 @@ expr parser::parse_notation(parse_table t, expr * left) {
                     throw parser_error(sstream() << "invalid composite expression, '" << *terminator << "' expected", pos());
                 }
             }
-            expr r   = instantiate_rev(copy_with_new_pos(a.get_initial(), p), args.size(), args.data());
             expr rec = copy_with_new_pos(a.get_rec(), p);
+            expr r;
             if (a.is_fold_right()) {
+                if (a.get_initial()) {
+                    r = instantiate_rev(copy_with_new_pos(*a.get_initial(), p), args.size(), args.data());
+                } else {
+                    r = r_args.back();
+                    r_args.pop_back();
+                }
                 unsigned i = r_args.size();
                 while (i > 0) {
                     --i;
@@ -915,7 +921,14 @@ expr parser::parse_notation(parse_table t, expr * left) {
                     args.pop_back(); args.pop_back();
                 }
             } else {
-                for (unsigned i = 0; i < r_args.size(); i++) {
+                unsigned fidx = 0;
+                if (a.get_initial()) {
+                    r = instantiate_rev(copy_with_new_pos(*a.get_initial(), p), args.size(), args.data());
+                } else {
+                    r = r_args[0];
+                    fidx++;
+                }
+                for (unsigned i = fidx; i < r_args.size(); i++) {
                     args.push_back(r_args[i]);
                     args.push_back(r);
                     r = instantiate_rev(rec, args.size(), args.data());
diff --git a/src/frontends/lean/parser_config.cpp b/src/frontends/lean/parser_config.cpp
index f56b1e681..7ea23d0f5 100644
--- a/src/frontends/lean/parser_config.cpp
+++ b/src/frontends/lean/parser_config.cpp
@@ -128,7 +128,12 @@ serializer & operator<<(serializer & s, action const & a) {
         s << a.rbp();
         break;
     case action_kind::Exprs:
-        s << a.get_sep() << a.get_rec() << a.get_initial() << a.is_fold_right() << a.rbp();
+        s << a.get_sep() << a.get_rec();
+        if (a.get_initial())
+            s << true << *a.get_initial();
+        else
+            s << false;
+        s << a.is_fold_right() << a.rbp();
         if (auto t = a.get_terminator()) {
             s << true << *t;
         } else {
@@ -161,8 +166,12 @@ action read_action(deserializer & d) {
         d >> rbp;
         return notation::mk_expr_action(rbp);
     case action_kind::Exprs: {
-        name sep; expr rec, ini; bool is_fold_right;
-        d >> sep >> rec >> ini >> is_fold_right >> rbp;
+        name sep; expr rec; optional<expr> ini; bool is_fold_right;
+        d >> sep >> rec;
+        if (d.read_bool()) {
+            ini = read_expr(d);
+        }
+        d >> is_fold_right >> rbp;
         optional<name> terminator;
         if (d.read_bool())
             terminator = read_name(d);
diff --git a/src/frontends/lean/pp.cpp b/src/frontends/lean/pp.cpp
index a8e9d39a6..286458718 100644
--- a/src/frontends/lean/pp.cpp
+++ b/src/frontends/lean/pp.cpp
@@ -808,7 +808,7 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
                     expr e = *args.back();
                     args.pop_back();
                     expr const & rec = a.get_rec();
-                    expr const & ini = a.get_initial();
+                    optional<expr> const & ini = a.get_initial();
                     buffer<expr> rec_args;
                     bool matched_once = false;
                     while (true) {
@@ -818,7 +818,6 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
                             args.pop_back();
                             break;
                         }
-                        matched_once = true;
                         optional<expr> new_e = args.back();
                         args.pop_back();
                         optional<expr> rec_arg = args.back();
@@ -827,11 +826,16 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
                             return optional<result>();
                         rec_args.push_back(*rec_arg);
                         e = *new_e;
+                        matched_once = true;
                     }
                     if (!matched_once)
                         return optional<result>();
-                    if (!match(ini, e, args))
-                        return optional<result>();
+                    if (ini) {
+                        if (!match(*ini, e, args))
+                            return optional<result>();
+                    } else {
+                        rec_args.push_back(e);
+                    }
                     if (!a.is_fold_right())
                         std::reverse(rec_args.begin(), rec_args.end());
                     unsigned curr_lbp = token_lbp;
@@ -847,9 +851,14 @@ auto pretty_fn::pp_notation(notation_entry const & entry, buffer<optional<expr>>
                     while (i > 0) {
                         --i;
                         result arg_res = pp_notation_child(rec_args[i], curr_lbp, a.rbp());
-                        if (i == 0)
-                            sep_fmt = format(tk);
-                        curr = sep_fmt + space() + arg_res.fmt() + curr;
+                        if (i == 0) {
+                            if (add_extra_space(tk))
+                                curr = format(tk) + space() + arg_res.fmt() + curr;
+                            else
+                                curr = format(tk) + arg_res.fmt() + curr;
+                        } else {
+                            curr = sep_fmt + space() + arg_res.fmt() + curr;
+                        }
                         if (i > 0 && add_extra_space(a.get_sep()))
                             curr = space() + curr;
                         curr_lbp = sep_lbp;
diff --git a/tests/lean/fold.lean b/tests/lean/fold.lean
new file mode 100644
index 000000000..1aa2f5039
--- /dev/null
+++ b/tests/lean/fold.lean
@@ -0,0 +1,31 @@
+import data.prod data.num
+
+variables a b c : num
+
+context
+  notation `(` t:(foldr `,` (e r, prod.mk e r)) `)` := t
+  check (a, false, b, true, c)
+  set_option pp.notation false
+  check (a, false, b, true, c)
+end
+
+context
+  notation `(` t:(foldr `,` (e r, prod.mk r e)) `)` := t
+  check (a, false, b, true, c)
+  set_option pp.notation false
+  check (a, false, b, true, c)
+end
+
+context
+  notation `(` t:(foldl `,` (e r, prod.mk r e)) `)` := t
+  check (a, false, b, true, c)
+  set_option pp.notation false
+  check (a, false, b, true, c)
+end
+
+context
+  notation `(` t:(foldl `,` (e r, prod.mk e r)) `)` := t
+  check (a, false, b, true, c)
+  set_option pp.notation false
+  check (a, false, b, true, c)
+end
diff --git a/tests/lean/fold.lean.expected.out b/tests/lean/fold.lean.expected.out
new file mode 100644
index 000000000..be434df08
--- /dev/null
+++ b/tests/lean/fold.lean.expected.out
@@ -0,0 +1,8 @@
+(a, false, b, true, c) : prod num (prod Prop (prod num (prod Prop num)))
+prod.mk a (prod.mk false (prod.mk b (prod.mk true c))) : prod num (prod Prop (prod num (prod Prop num)))
+(a, false, b, true, c) : prod (prod (prod (prod num Prop) num) Prop) num
+prod.mk (prod.mk (prod.mk (prod.mk c true) b) false) a : prod (prod (prod (prod num Prop) num) Prop) num
+(a, false, b, true, c) : prod (prod (prod (prod num Prop) num) Prop) num
+prod.mk (prod.mk (prod.mk (prod.mk a false) b) true) c : prod (prod (prod (prod num Prop) num) Prop) num
+(a, false, b, true, c) : prod num (prod Prop (prod num (prod Prop num)))
+prod.mk c (prod.mk true (prod.mk b (prod.mk false a))) : prod num (prod Prop (prod num (prod Prop num)))