diff --git a/src/frontends/lean/CMakeLists.txt b/src/frontends/lean/CMakeLists.txt
index f353721ab..b5eab1e4b 100644
--- a/src/frontends/lean/CMakeLists.txt
+++ b/src/frontends/lean/CMakeLists.txt
@@ -1,4 +1,4 @@
-add_library(lean_frontend register_module.cpp token_set.cpp
+add_library(lean_frontend register_module.cpp token_table.cpp
 scanner.cpp parse_table.cpp)
 
 target_link_libraries(lean_frontend ${LEAN_LIBS})
diff --git a/src/frontends/lean/parse_table.h b/src/frontends/lean/parse_table.h
index 441d0cf75..bc00227ba 100644
--- a/src/frontends/lean/parse_table.h
+++ b/src/frontends/lean/parse_table.h
@@ -9,7 +9,7 @@ Author: Leonardo de Moura
 #include "util/buffer.h"
 #include "util/lua.h"
 #include "kernel/expr.h"
-#include "frontends/lean/token_set.h"
+#include "frontends/lean/token_table.h"
 
 namespace lean {
 class parser_context;
diff --git a/src/frontends/lean/register_module.cpp b/src/frontends/lean/register_module.cpp
index 3cb528c27..4a94ca7b7 100644
--- a/src/frontends/lean/register_module.cpp
+++ b/src/frontends/lean/register_module.cpp
@@ -7,12 +7,12 @@ Author: Leonardo de Moura
 #include <sstream>
 #include "util/lua.h"
 #include "util/script_state.h"
-#include "frontends/lean/token_set.h"
+#include "frontends/lean/token_table.h"
 #include "frontends/lean/parse_table.h"
 
 namespace lean {
 void open_frontend_lean(lua_State * L) {
-    open_token_set(L);
+    open_token_table(L);
     open_parse_table(L);
 }
 void register_frontend_lean_module() {
diff --git a/src/frontends/lean/scanner.cpp b/src/frontends/lean/scanner.cpp
index 9f9579b2e..c23f2486c 100644
--- a/src/frontends/lean/scanner.cpp
+++ b/src/frontends/lean/scanner.cpp
@@ -211,7 +211,7 @@ auto scanner::read_key_cmd_id() -> token_kind {
     static char const * error_msg = "unexpected token";
     char c = curr();
     unsigned num_cs = 1; // number of characters read
-    token_set const * it    = find(m_tokens, c);
+    token_table const * it    = find(m_tokens, c);
     token_info const * info = nullptr;
     unsigned key_size       = 0;
     if (it) {
@@ -318,7 +318,7 @@ auto scanner::scan() -> token_kind {
     }
 }
 
-scanner::scanner(token_set const & tks, std::istream & strm, char const * strm_name):
+scanner::scanner(token_table const & tks, std::istream & strm, char const * strm_name):
     m_tokens(tks), m_stream(strm), m_spos(0), m_sline(1), m_curr(0), m_pos(0), m_line(1),
     m_token_info(nullptr) {
     m_stream_name = strm_name ? strm_name : "[unknown]";
diff --git a/src/frontends/lean/scanner.h b/src/frontends/lean/scanner.h
index 8f011bf83..d4f4612aa 100644
--- a/src/frontends/lean/scanner.h
+++ b/src/frontends/lean/scanner.h
@@ -8,7 +8,7 @@ Author: Leonardo de Moura
 #include <iostream>
 #include "util/name.h"
 #include "util/numerics/mpq.h"
-#include "frontends/lean/token_set.h"
+#include "frontends/lean/token_table.h"
 
 namespace lean {
 /**
@@ -22,7 +22,7 @@ class scanner {
 public:
     enum class token_kind {Keyword, CommandKeyword, ScriptBlock, Identifier, Numeral, Decimal, String, Eof};
 protected:
-    token_set          m_tokens;
+    token_table        m_tokens;
     std::istream &     m_stream;
     std::string        m_stream_name;
 
@@ -60,7 +60,7 @@ protected:
     token_kind read_key_cmd_id();
 
 public:
-    scanner(token_set const & tks, std::istream & strm, char const * strm_name = nullptr);
+    scanner(token_table const & tks, std::istream & strm, char const * strm_name = nullptr);
 
     int get_line() const { return m_line; }
     int get_pos() const { return m_pos; }
diff --git a/src/frontends/lean/token_set.cpp b/src/frontends/lean/token_table.cpp
similarity index 62%
rename from src/frontends/lean/token_set.cpp
rename to src/frontends/lean/token_table.cpp
index ac5439ad2..59bd65e3a 100644
--- a/src/frontends/lean/token_set.cpp
+++ b/src/frontends/lean/token_table.cpp
@@ -5,28 +5,28 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #include <utility>
-#include "frontends/lean/token_set.h"
+#include "frontends/lean/token_table.h"
 
 namespace lean {
-token_set add_command_token(token_set const & s, char const * token) {
+token_table add_command_token(token_table const & s, char const * token) {
     return insert(s, token, token_info(token));
 }
-token_set add_command_token(token_set const & s, char const * token, char const * val) {
+token_table add_command_token(token_table const & s, char const * token, char const * val) {
     return insert(s, token, token_info(val));
 }
-token_set add_token(token_set const & s, char const * token, unsigned prec) {
+token_table add_token(token_table const & s, char const * token, unsigned prec) {
     return insert(s, token, token_info(token, prec));
 }
-token_set add_token(token_set const & s, char const * token, char const * val, unsigned prec) {
+token_table add_token(token_table const & s, char const * token, char const * val, unsigned prec) {
     return insert(s, token, token_info(val, prec));
 }
-token_set const * find(token_set const & s, char c) {
+token_table const * find(token_table const & s, char c) {
     return s.find(c);
 }
-token_info const * value_of(token_set const & s) {
+token_info const * value_of(token_table const & s) {
     return s.value();
 }
-void for_each(token_set const & s, std::function<void(char const *, token_info const &)> const & fn) {
+void for_each(token_table const & s, std::function<void(char const *, token_info const &)> const & fn) {
     s.for_each([&](unsigned num, char const * keys, token_info const & info) {
             buffer<char> str;
             str.append(num, keys);
@@ -41,10 +41,10 @@ static char const * g_forall_unicode = "\u2200";
 static char const * g_arrow_unicode  = "\u2192";
 
 // Auxiliary class for creating the initial token set
-class init_token_set_fn {
+class init_token_table_fn {
 public:
-    token_set m_token_set;
-    init_token_set_fn() {
+    token_table m_token_table;
+    init_token_table_fn() {
             char const * builtin[] = {"fun", "Pi", "let", "in", "have", "show", "by", "from", "(", ")", "{", "}",
                                       ".{", "Type", "...", ",", ".", ":", "calc", ":=", "--", "(*", "(--", "->",
                                       "proof", "qed", "private", nullptr};
@@ -64,52 +64,52 @@ public:
 
             auto it = builtin;
             while (*it) {
-                m_token_set = add_token(m_token_set, *it);
+                m_token_table = add_token(m_token_table, *it);
                 it++;
             }
 
             it = commands;
             while (*it) {
-                m_token_set = add_command_token(m_token_set, *it);
+                m_token_table = add_command_token(m_token_table, *it);
                 ++it;
             }
 
             auto it2 = aliases;
             while (it2->first) {
-                m_token_set = add_token(m_token_set, it2->first, it2->second);
+                m_token_table = add_token(m_token_table, it2->first, it2->second);
                 it2++;
             }
 
             it2 = cmd_aliases;
             while (it2->first) {
-                m_token_set = add_command_token(m_token_set, it2->first, it2->second);
+                m_token_table = add_command_token(m_token_table, it2->first, it2->second);
                 ++it2;
             }
     }
 };
-static init_token_set_fn g_init;
-token_set mk_token_set() { return token_set(); }
-token_set mk_default_token_set() { return g_init.m_token_set; }
+static init_token_table_fn g_init;
+token_table mk_token_table() { return token_table(); }
+token_table mk_default_token_table() { return g_init.m_token_table; }
 
-DECL_UDATA(token_set)
-static int mk_token_set(lua_State * L) { return push_token_set(L, mk_token_set()); }
-static int mk_default_token_set(lua_State * L) { return push_token_set(L, mk_default_token_set()); }
+DECL_UDATA(token_table)
+static int mk_token_table(lua_State * L) { return push_token_table(L, mk_token_table()); }
+static int mk_default_token_table(lua_State * L) { return push_token_table(L, mk_default_token_table()); }
 static int add_command_token(lua_State * L) {
     int nargs = lua_gettop(L);
     if (nargs == 2)
-        return push_token_set(L, add_command_token(to_token_set(L, 1), lua_tostring(L, 2)));
+        return push_token_table(L, add_command_token(to_token_table(L, 1), lua_tostring(L, 2)));
     else
-        return push_token_set(L, add_command_token(to_token_set(L, 1), lua_tostring(L, 2), lua_tostring(L, 3)));
+        return push_token_table(L, add_command_token(to_token_table(L, 1), lua_tostring(L, 2), lua_tostring(L, 3)));
 }
 static int add_token(lua_State * L) {
     int nargs = lua_gettop(L);
     if (nargs == 3)
-        return push_token_set(L, add_token(to_token_set(L, 1), lua_tostring(L, 2), lua_tonumber(L, 3)));
+        return push_token_table(L, add_token(to_token_table(L, 1), lua_tostring(L, 2), lua_tonumber(L, 3)));
     else
-        return push_token_set(L, add_token(to_token_set(L, 1), lua_tostring(L, 2), lua_tostring(L, 3), lua_tonumber(L, 4)));
+        return push_token_table(L, add_token(to_token_table(L, 1), lua_tostring(L, 2), lua_tostring(L, 3), lua_tonumber(L, 4)));
 }
 static int merge(lua_State * L) {
-    return push_token_set(L, merge(to_token_set(L, 1), to_token_set(L, 2)));
+    return push_token_table(L, merge(to_token_table(L, 1), to_token_table(L, 2)));
 }
 static int find(lua_State * L) {
     char k;
@@ -121,14 +121,14 @@ static int find(lua_State * L) {
             throw exception("arg #2 must be a string of length 1");
         k = str[0];
     }
-    auto it = to_token_set(L, 1).find(k);
+    auto it = to_token_table(L, 1).find(k);
     if (it)
-        return push_token_set(L, *it);
+        return push_token_table(L, *it);
     else
         return push_nil(L);
 }
 static int value_of(lua_State * L) {
-    auto it = value_of(to_token_set(L, 1));
+    auto it = value_of(to_token_table(L, 1));
     if (it) {
         push_boolean(L, it->is_command());
         push_name(L, it->value());
@@ -140,7 +140,7 @@ static int value_of(lua_State * L) {
     }
 }
 static int for_each(lua_State * L) {
-    token_set const & t = to_token_set(L, 1);
+    token_table const & t = to_token_table(L, 1);
     luaL_checktype(L, 2, LUA_TFUNCTION); // user-fun
     for_each(t, [&](char const * k, token_info const & info) {
             lua_pushvalue(L, 2);
@@ -153,8 +153,8 @@ static int for_each(lua_State * L) {
     return 0;
 }
 
-static const struct luaL_Reg token_set_m[] = {
-    {"__gc",              token_set_gc},
+static const struct luaL_Reg token_table_m[] = {
+    {"__gc",              token_table_gc},
     {"add_command_token", safe_function<add_command_token>},
     {"add_token",         safe_function<add_token>},
     {"merge",             safe_function<merge>},
@@ -164,14 +164,14 @@ static const struct luaL_Reg token_set_m[] = {
     {0, 0}
 };
 
-void open_token_set(lua_State * L) {
-    luaL_newmetatable(L, token_set_mt);
+void open_token_table(lua_State * L) {
+    luaL_newmetatable(L, token_table_mt);
     lua_pushvalue(L, -1);
     lua_setfield(L, -2, "__index");
-    setfuncs(L, token_set_m, 0);
+    setfuncs(L, token_table_m, 0);
 
-    SET_GLOBAL_FUN(token_set_pred,       "is_token_set");
-    SET_GLOBAL_FUN(mk_default_token_set, "default_token_set");
-    SET_GLOBAL_FUN(mk_token_set,         "token_set");
+    SET_GLOBAL_FUN(token_table_pred,       "is_token_table");
+    SET_GLOBAL_FUN(mk_default_token_table, "default_token_table");
+    SET_GLOBAL_FUN(mk_token_table,         "token_table");
 }
 }
diff --git a/src/frontends/lean/token_set.h b/src/frontends/lean/token_table.h
similarity index 52%
rename from src/frontends/lean/token_set.h
rename to src/frontends/lean/token_table.h
index c7534bc5c..fe56050a7 100644
--- a/src/frontends/lean/token_set.h
+++ b/src/frontends/lean/token_table.h
@@ -25,15 +25,15 @@ public:
     unsigned precedence() const { return m_precedence; }
 };
 
-typedef ctrie<token_info> token_set;
-token_set mk_token_set();
-token_set mk_default_token_set();
-token_set add_command_token(token_set const & s, char const * token);
-token_set add_command_token(token_set const & s, char const * token, char const * val);
-token_set add_token(token_set const & s, char const * token, unsigned prec = 0);
-token_set add_token(token_set const & s, char const * token, char const * val, unsigned prec = 0);
-void for_each(token_set const & s, std::function<void(char const *, token_info const&)> const & fn);
-token_set const * find(token_set const & s, char c);
-token_info const * value_of(token_set const & s);
-void open_token_set(lua_State * L);
+typedef ctrie<token_info> token_table;
+token_table mk_token_table();
+token_table mk_default_token_table();
+token_table add_command_token(token_table const & s, char const * token);
+token_table add_command_token(token_table const & s, char const * token, char const * val);
+token_table add_token(token_table const & s, char const * token, unsigned prec = 0);
+token_table add_token(token_table const & s, char const * token, char const * val, unsigned prec = 0);
+void for_each(token_table const & s, std::function<void(char const *, token_info const&)> const & fn);
+token_table const * find(token_table const & s, char c);
+token_info const * value_of(token_table const & s);
+void open_token_table(lua_State * L);
 }
diff --git a/src/tests/frontends/lean/scanner.cpp b/src/tests/frontends/lean/scanner.cpp
index d43975047..79afb254f 100644
--- a/src/tests/frontends/lean/scanner.cpp
+++ b/src/tests/frontends/lean/scanner.cpp
@@ -13,7 +13,7 @@ using namespace lean;
 
 #define tk scanner::token_kind
 
-static void scan(char const * str, token_set set = mk_default_token_set()) {
+static void scan(char const * str, token_table set = mk_default_token_table()) {
     std::istringstream in(str);
     scanner s(set, in, "[string]");
     while (true) {
@@ -35,7 +35,7 @@ static void scan(char const * str, token_set set = mk_default_token_set()) {
     std::cout << "\n";
 }
 
-static void scan_success(char const * str, token_set set = mk_default_token_set()) {
+static void scan_success(char const * str, token_table set = mk_default_token_table()) {
     try {
         scan(str, set);
     } catch (exception & ex) {
@@ -54,7 +54,7 @@ static void scan_error(char const * str) {
 }
 
 static void check(char const * str, std::initializer_list<tk> const & l,
-                  token_set set = mk_default_token_set()) {
+                  token_table set = mk_default_token_table()) {
     try {
         auto it = l.begin();
         std::istringstream in(str);
@@ -75,7 +75,7 @@ static void check(char const * str, std::initializer_list<tk> const & l,
     }
 }
 
-static void check_name(char const * str, name const & expected, token_set set = mk_default_token_set()) {
+static void check_name(char const * str, name const & expected, token_table set = mk_default_token_table()) {
     std::istringstream in(str);
     scanner s(set, in, "[string]");
     tk k = s.scan();
@@ -84,7 +84,7 @@ static void check_name(char const * str, name const & expected, token_set set =
     lean_assert(s.scan() == tk::Eof);
 }
 
-static void check_keyword(char const * str, name const & expected, token_set set = mk_default_token_set()) {
+static void check_keyword(char const * str, name const & expected, token_table set = mk_default_token_table()) {
     std::istringstream in(str);
     scanner s(set, in, "[string]");
     tk k = s.scan();
@@ -94,7 +94,7 @@ static void check_keyword(char const * str, name const & expected, token_set set
 }
 
 static void tst1() {
-    token_set s = mk_default_token_set();
+    token_table s = mk_default_token_table();
     s = add_token(s, "+", "plus");
     s = add_token(s, "=", "eq");
     scan_success("a..a");
@@ -133,7 +133,7 @@ static void tst2() {
     check_name("x.bla", name({"x", "bla"}));
 
     scan_error("+++");
-    token_set s = mk_default_token_set();
+    token_table s = mk_default_token_table();
     s = add_token(s, "+++", "tplus");
     check_keyword("+++", "tplus", s);
     s = add_token(s, "+", "plus");
diff --git a/tests/lua/token_set.lua b/tests/lua/token_table.lua
similarity index 62%
rename from tests/lua/token_set.lua
rename to tests/lua/token_table.lua
index 971dda7e9..890dbb9a5 100644
--- a/tests/lua/token_set.lua
+++ b/tests/lua/token_table.lua
@@ -1,4 +1,4 @@
-function display_token_set(s)
+function display_token_table(s)
    s:for_each(function(k, cmd, val, prec)
                  io.write(k)
                  if cmd then
@@ -8,15 +8,15 @@ function display_token_set(s)
    end)
 end
 
-function token_set_size(s)
+function token_table_size(s)
    local r = 0
    s:for_each(function() r = r + 1 end)
    return r
 end
 
-local s = token_set()
-assert(is_token_set(s))
-assert(token_set_size(s) == 0)
+local s = token_table()
+assert(is_token_table(s))
+assert(token_table_size(s) == 0)
 s = s:add_command_token("test",  "tst1")
 s = s:add_command_token("tast",  "tst2")
 s = s:add_command_token("tests", "tst3")
@@ -24,22 +24,22 @@ s = s:add_command_token("fests", "tst4")
 s = s:add_command_token("tes",   "tst5")
 s = s:add_token("++", "++", 65)
 s = s:add_token("++-", "plusminus")
-assert(token_set_size(s) == 7)
-display_token_set(s)
+assert(token_table_size(s) == 7)
+display_token_table(s)
 
 
 print("========")
-local s2 = default_token_set()
-display_token_set(s2)
-assert(token_set_size(s2) > 0)
-local sz1 = token_set_size(s)
-local sz2 = token_set_size(s2)
+local s2 = default_token_table()
+display_token_table(s2)
+assert(token_table_size(s2) > 0)
+local sz1 = token_table_size(s)
+local sz2 = token_table_size(s2)
 s2 = s2:merge(s)
-assert(token_set_size(s2) == sz1 + sz2)
+assert(token_table_size(s2) == sz1 + sz2)
 s2 = s2:find("t"):find("e")
 print("========")
-display_token_set(s2)
-assert(token_set_size(s2) == 3)
+display_token_table(s2)
+assert(token_table_size(s2) == 3)
 s2 = s2:find("s")
 local cmd, val, prec = s2:value_of()
 assert(val == name("tst5"))