diff --git a/hott/init/tactic.hlean b/hott/init/tactic.hlean
index 397c9723d..42d8b8221 100644
--- a/hott/init/tactic.hlean
+++ b/hott/init/tactic.hlean
@@ -68,7 +68,7 @@ opaque definition apply      (e : expr)            : tactic := builtin
 opaque definition fapply     (e : expr)            : tactic := builtin
 opaque definition rename     (a b : identifier)    : tactic := builtin
 opaque definition intro      (e : identifier_list) : tactic := builtin
-opaque definition generalize (e : expr)            : tactic := builtin
+opaque definition generalize_tac (e : expr) (id : identifier) : tactic := builtin
 opaque definition clear      (e : identifier_list) : tactic := builtin
 opaque definition revert     (e : identifier_list) : tactic := builtin
 opaque definition refine     (e : expr)            : tactic := builtin
diff --git a/library/init/tactic.lean b/library/init/tactic.lean
index 998225af6..de1a049a0 100644
--- a/library/init/tactic.lean
+++ b/library/init/tactic.lean
@@ -68,7 +68,7 @@ opaque definition apply      (e : expr)         : tactic := builtin
 opaque definition fapply     (e : expr)         : tactic := builtin
 opaque definition rename     (a b : identifier) : tactic := builtin
 opaque definition intro      (e : identifier_list) : tactic := builtin
-opaque definition generalize (e : expr)            : tactic := builtin
+opaque definition generalize_tac (e : expr) (id : identifier) : tactic := builtin
 opaque definition clear      (e : identifier_list) : tactic := builtin
 opaque definition revert     (e : identifier_list) : tactic := builtin
 opaque definition refine     (e : expr)         : tactic := builtin
diff --git a/src/frontends/lean/builtin_tactics.cpp b/src/frontends/lean/builtin_tactics.cpp
index c43e8b1b2..becbbc170 100644
--- a/src/frontends/lean/builtin_tactics.cpp
+++ b/src/frontends/lean/builtin_tactics.cpp
@@ -5,6 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #include "library/tactic/let_tactic.h"
+#include "library/tactic/generalize_tactic.h"
 #include "frontends/lean/tokens.h"
 #include "frontends/lean/parser.h"
 #include "frontends/lean/parse_rewrite_tactic.h"
@@ -38,16 +39,34 @@ static expr parse_let_tactic(parser & p, unsigned, expr const *, pos_info const
     return p.save_pos(mk_let_tactic_expr(id, value), pos);
 }
 
+static expr parse_generalize_tactic(parser & p, unsigned, expr const *, pos_info const & pos) {
+    expr e = p.parse_expr();
+    name id;
+    if (p.curr_is_token(get_as_tk())) {
+        p.next();
+        id = p.check_atomic_id_next("invalid 'generalize' tactic, identifier expected");
+    } else {
+        if (is_constant(e))
+            id = const_name(e);
+        else if (is_local(e))
+            id = local_pp_name(e);
+        else
+            id = name("x");
+    }
+    return p.save_pos(mk_generalize_tactic_expr(e, id), pos);
+}
+
 parse_table init_tactic_nud_table() {
     action Expr(mk_expr_action());
     expr x0 = mk_var(0);
     parse_table r;
     r = r.add({transition("(", Expr), transition(")", mk_ext_action(parse_rparen))}, x0);
-    r = r.add({transition("rewrite", mk_ext_action(parse_rewrite_tactic_expr))}, x0);
-    r = r.add({transition("esimp",   mk_ext_action(parse_esimp_tactic_expr))}, x0);
-    r = r.add({transition("unfold",  mk_ext_action(parse_unfold_tactic_expr))}, x0);
-    r = r.add({transition("fold",    mk_ext_action(parse_fold_tactic_expr))}, x0);
-    r = r.add({transition("let",    mk_ext_action(parse_let_tactic))}, x0);
+    r = r.add({transition("rewrite",    mk_ext_action(parse_rewrite_tactic_expr))}, x0);
+    r = r.add({transition("esimp",      mk_ext_action(parse_esimp_tactic_expr))}, x0);
+    r = r.add({transition("generalize", mk_ext_action(parse_generalize_tactic))}, x0);
+    r = r.add({transition("unfold",     mk_ext_action(parse_unfold_tactic_expr))}, x0);
+    r = r.add({transition("fold",       mk_ext_action(parse_fold_tactic_expr))}, x0);
+    r = r.add({transition("let",        mk_ext_action(parse_let_tactic))}, x0);
     return r;
 }
 
diff --git a/src/frontends/lean/token_table.cpp b/src/frontends/lean/token_table.cpp
index 50245cc87..f7f48c4a8 100644
--- a/src/frontends/lean/token_table.cpp
+++ b/src/frontends/lean/token_table.cpp
@@ -95,6 +95,7 @@ void init_token_table(token_table & t) {
          {"{|", g_max_prec}, {"|}", 0}, {"⊢", 0}, {"⟨", g_max_prec}, {"⟩", 0}, {"^", 0}, {"↑", 0}, {"▸", 0},
          {"using", 0}, {"|", 0}, {"!", g_max_prec}, {"?", 0},  {"with", 0}, {"...", 0}, {",", 0},
          {".", 0}, {":", 0}, {"::", 0}, {"calc", 0}, {"rewrite", 0}, {"esimp", 0}, {"fold", 0}, {"unfold", 0},
+         {"generalize", 0}, {"as", 0},
          {":=", 0}, {"--", 0}, {"#", 0},
          {"(*", 0}, {"/-", 0}, {"begin", g_max_prec}, {"proof", g_max_prec}, {"qed", 0}, {"@", g_max_prec},
          {"sorry", g_max_prec}, {"+", g_plus_prec}, {g_cup, g_cup_prec}, {"->", g_arrow_prec},
diff --git a/src/library/constants.cpp b/src/library/constants.cpp
index 76ad7d3d3..0127b3769 100644
--- a/src/library/constants.cpp
+++ b/src/library/constants.cpp
@@ -91,7 +91,7 @@ name const * g_tactic_opt_identifier_list = nullptr;
 name const * g_tactic_fail = nullptr;
 name const * g_tactic_fixpoint = nullptr;
 name const * g_tactic_focus_at = nullptr;
-name const * g_tactic_generalize = nullptr;
+name const * g_tactic_generalize_tac = nullptr;
 name const * g_tactic_generalizes = nullptr;
 name const * g_tactic_id = nullptr;
 name const * g_tactic_interleave = nullptr;
@@ -210,7 +210,7 @@ void initialize_constants() {
     g_tactic_fail = new name{"tactic", "fail"};
     g_tactic_fixpoint = new name{"tactic", "fixpoint"};
     g_tactic_focus_at = new name{"tactic", "focus_at"};
-    g_tactic_generalize = new name{"tactic", "generalize"};
+    g_tactic_generalize_tac = new name{"tactic", "generalize_tac"};
     g_tactic_generalizes = new name{"tactic", "generalizes"};
     g_tactic_id = new name{"tactic", "id"};
     g_tactic_interleave = new name{"tactic", "interleave"};
@@ -330,7 +330,7 @@ void finalize_constants() {
     delete g_tactic_fail;
     delete g_tactic_fixpoint;
     delete g_tactic_focus_at;
-    delete g_tactic_generalize;
+    delete g_tactic_generalize_tac;
     delete g_tactic_generalizes;
     delete g_tactic_id;
     delete g_tactic_interleave;
@@ -449,7 +449,7 @@ name const & get_tactic_opt_identifier_list_name() { return *g_tactic_opt_identi
 name const & get_tactic_fail_name() { return *g_tactic_fail; }
 name const & get_tactic_fixpoint_name() { return *g_tactic_fixpoint; }
 name const & get_tactic_focus_at_name() { return *g_tactic_focus_at; }
-name const & get_tactic_generalize_name() { return *g_tactic_generalize; }
+name const & get_tactic_generalize_tac_name() { return *g_tactic_generalize_tac; }
 name const & get_tactic_generalizes_name() { return *g_tactic_generalizes; }
 name const & get_tactic_id_name() { return *g_tactic_id; }
 name const & get_tactic_interleave_name() { return *g_tactic_interleave; }
diff --git a/src/library/constants.h b/src/library/constants.h
index 4709ad49d..bc1c7a964 100644
--- a/src/library/constants.h
+++ b/src/library/constants.h
@@ -93,7 +93,7 @@ name const & get_tactic_opt_identifier_list_name();
 name const & get_tactic_fail_name();
 name const & get_tactic_fixpoint_name();
 name const & get_tactic_focus_at_name();
-name const & get_tactic_generalize_name();
+name const & get_tactic_generalize_tac_name();
 name const & get_tactic_generalizes_name();
 name const & get_tactic_id_name();
 name const & get_tactic_interleave_name();
diff --git a/src/library/constants.txt b/src/library/constants.txt
index bb0be82c8..b5b2266e6 100644
--- a/src/library/constants.txt
+++ b/src/library/constants.txt
@@ -86,7 +86,7 @@ tactic.opt_identifier_list
 tactic.fail
 tactic.fixpoint
 tactic.focus_at
-tactic.generalize
+tactic.generalize_tac
 tactic.generalizes
 tactic.id
 tactic.interleave
diff --git a/src/library/tactic/generalize_tactic.cpp b/src/library/tactic/generalize_tactic.cpp
index 3ee31884a..b8ca55ff3 100644
--- a/src/library/tactic/generalize_tactic.cpp
+++ b/src/library/tactic/generalize_tactic.cpp
@@ -12,6 +12,11 @@ Author: Leonardo de Moura
 #include "library/tactic/expr_to_tactic.h"
 
 namespace lean {
+expr mk_generalize_tactic_expr(expr const & e, name const & id) {
+    return mk_app(mk_constant(get_tactic_generalize_tac_name()),
+                  e, mk_constant(id));
+}
+
 tactic generalize_tactic(elaborate_fn const & elab, expr const & e, name const & x) {
     return tactic01([=](environment const & env, io_state const & ios, proof_state const & s) {
             proof_state new_s = s;
@@ -60,11 +65,11 @@ tactic generalize_tactic(elaborate_fn const & elab, expr const & e, name const &
 }
 
 void initialize_generalize_tactic() {
-    register_tac(get_tactic_generalize_name(),
+    register_tac(get_tactic_generalize_tac_name(),
                  [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
-                     check_tactic_expr(app_arg(e), "invalid 'generalize' tactic, invalid argument");
-                     // TODO(Leo): allow user to provide name to abstract variable
-                     return generalize_tactic(fn, get_tactic_expr_expr(app_arg(e)), "x");
+                     check_tactic_expr(app_arg(app_fn(e)), "invalid 'generalize' tactic, invalid argument");
+                     name id = tactic_expr_to_id(app_arg(e), "invalid 'generalize' tactic, argument must be an identifier");
+                     return generalize_tactic(fn, get_tactic_expr_expr(app_arg(app_fn(e))), id);
                  });
 
     register_tac(get_tactic_generalizes_name(),
diff --git a/src/library/tactic/generalize_tactic.h b/src/library/tactic/generalize_tactic.h
index ad74f1b22..03daddf41 100644
--- a/src/library/tactic/generalize_tactic.h
+++ b/src/library/tactic/generalize_tactic.h
@@ -8,7 +8,7 @@ Author: Leonardo de Moura
 #include "library/tactic/elaborate.h"
 
 namespace lean {
-tactic generalize_tactic(elaborate_fn const & elab, expr const & e);
+expr mk_generalize_tactic_expr(expr const & e, name const & id);
 void initialize_generalize_tactic();
 void finalize_generalize_tactic();
 }
diff --git a/tests/lean/gen_as.lean b/tests/lean/gen_as.lean
new file mode 100644
index 000000000..7a7756a2c
--- /dev/null
+++ b/tests/lean/gen_as.lean
@@ -0,0 +1,9 @@
+import data.nat
+open nat
+
+example (x y : nat) : x + y + y ≥ 0 :=
+begin
+  generalize x + y + y as n,
+  state,
+  intro n, exact zero_le n
+end
diff --git a/tests/lean/gen_as.lean.expected.out b/tests/lean/gen_as.lean.expected.out
new file mode 100644
index 000000000..7be3850cf
--- /dev/null
+++ b/tests/lean/gen_as.lean.expected.out
@@ -0,0 +1,4 @@
+gen_as.lean:7:2: proof state
+x y : ℕ
+⊢ ∀ (n : ℕ),
+    n ≥ 0