diff --git a/src/library/coercion.cpp b/src/library/coercion.cpp
index f6c1f90de..90f5c2d23 100644
--- a/src/library/coercion.cpp
+++ b/src/library/coercion.cpp
@@ -12,6 +12,7 @@ Author: Leonardo de Moura
 #include "library/coercion.h"
 #include "library/module.h"
 #include "library/kernel_serializer.h"
+#include "library/kernel_bindings.h"
 
 namespace lean {
 enum class coercion_class_kind { User, Sort, Fun };
@@ -408,4 +409,59 @@ bool get_user_coercions(environment const & env, expr const & C, buffer<std::pai
     }
     return r;
 }
+
+static int add_coercion(lua_State * L) {
+    int nargs = lua_gettop(L);
+    if (nargs == 2)
+        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), get_io_state(L)));
+    else if (nargs == 3 && is_io_state(L, 3))
+        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_io_state(L, 3)));
+    else if (nargs == 3)
+        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), get_io_state(L)));
+    else
+        return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), to_io_state(L, 4)));
+}
+static int is_coercion(lua_State * L) { return push_boolean(L, is_coercion(to_environment(L, 1), to_expr(L, 2))); }
+static int has_coercions_from(lua_State * L) {
+    if (is_expr(L, 2))
+        return push_boolean(L, has_coercions_from(to_environment(L, 1), to_expr(L, 2)));
+    else
+        return push_boolean(L, has_coercions_from(to_environment(L, 1), to_name_ext(L, 2)));
+}
+static int has_coercions_to(lua_State * L) {
+    if (is_expr(L, 2))
+        return push_boolean(L, has_coercions_to(to_environment(L, 1), to_expr(L, 2)));
+    else
+        return push_boolean(L, has_coercions_to(to_environment(L, 1), to_name_ext(L, 2)));
+}
+static int get_coercion(lua_State * L) { return push_optional_expr(L, get_coercion(to_environment(L, 1), to_expr(L, 2), to_name_ext(L, 3))); }
+static int get_coercion_to_sort(lua_State * L) { return push_optional_expr(L, get_coercion_to_sort(to_environment(L, 1), to_expr(L, 2))); }
+static int get_coercion_to_fun(lua_State * L) { return push_optional_expr(L, get_coercion_to_fun(to_environment(L, 1), to_expr(L, 2))); }
+static int get_user_coercions(lua_State * L) {
+    buffer<std::pair<expr, name>> r;
+    get_user_coercions(to_environment(L, 1), to_expr(L, 2), r);
+    lua_newtable(L);
+    int i = 1;
+    for (auto p : r) {
+        lua_newtable(L);
+        push_expr(L, p.first);
+        lua_rawseti(L, -2, 1);
+        push_name(L, p.second);
+        lua_rawseti(L, -2, 2);
+        lua_rawseti(L, -2, i);
+        i = i + 1;
+    }
+    return 1;
+}
+
+void open_coercion(lua_State * L) {
+    SET_GLOBAL_FUN(add_coercion,         "add_coercion");
+    SET_GLOBAL_FUN(is_coercion,          "is_coercion");
+    SET_GLOBAL_FUN(has_coercions_from,   "has_coercions_from");
+    SET_GLOBAL_FUN(has_coercions_to,     "has_coercions_to");
+    SET_GLOBAL_FUN(get_coercion,         "get_coercion");
+    SET_GLOBAL_FUN(get_coercion_to_sort, "get_coercion_to_sort");
+    SET_GLOBAL_FUN(get_coercion_to_fun,  "get_coercion_to_fun");
+    SET_GLOBAL_FUN(get_user_coercions,   "get_user_coercions");
+}
 }
diff --git a/src/library/coercion.h b/src/library/coercion.h
index 462baffcc..4bb90d821 100644
--- a/src/library/coercion.h
+++ b/src/library/coercion.h
@@ -6,6 +6,7 @@ Author: Leonardo de Moura
 */
 #pragma once
 #include <utility>
+#include "util/lua.h"
 #include "kernel/environment.h"
 #include "library/expr_pair.h"
 #include "library/io_state.h"
@@ -60,4 +61,6 @@ optional<expr> get_coercion_to_fun(environment const & env, expr const & C);
    \remark The most recent coercions occur first.
 */
 bool get_user_coercions(environment const & env, expr const & C, buffer<std::pair<expr, name>> & result);
+
+void open_coercion(lua_State * L);
 }
diff --git a/src/library/kernel_bindings.cpp b/src/library/kernel_bindings.cpp
index 3ec2eb04a..9a9a26fb7 100644
--- a/src/library/kernel_bindings.cpp
+++ b/src/library/kernel_bindings.cpp
@@ -42,8 +42,14 @@ Author: Leonardo de Moura
 
 namespace lean {
 static environment get_global_environment(lua_State * L);
-io_state * get_io_state(lua_State * L);
+io_state * get_io_state_ptr(lua_State * L);
 io_state get_tmp_io_state(lua_State * L);
+io_state get_io_state(lua_State * L) {
+    if (io_state * ios = get_io_state_ptr(L))
+        return *ios;
+    else
+        return get_tmp_io_state(L);
+}
 
 // Level
 DECL_UDATA(level)
@@ -983,7 +989,7 @@ static char g_formatter_key;
 static formatter g_simple_formatter = mk_simple_formatter();
 
 optional<formatter> get_global_formatter_core(lua_State * L) {
-    io_state * io = get_io_state(L);
+    io_state * io = get_io_state_ptr(L);
     if (io != nullptr) {
         return optional<formatter>(io->get_formatter());
     } else {
@@ -1009,7 +1015,7 @@ formatter get_global_formatter(lua_State * L) {
 }
 
 void set_global_formatter(lua_State * L, formatter const & fmt) {
-    io_state * io = get_io_state(L);
+    io_state * io = get_io_state_ptr(L);
     if (io != nullptr) {
         io->set_formatter(fmt);
     } else {
@@ -1020,7 +1026,7 @@ void set_global_formatter(lua_State * L, formatter const & fmt) {
 }
 
 static int get_formatter(lua_State * L) {
-    io_state * io = get_io_state(L);
+    io_state * io = get_io_state_ptr(L);
     if (io != nullptr) {
         return push_formatter(L, io->get_formatter());
     } else {
@@ -1168,10 +1174,8 @@ static int import_modules(environment const & env, lua_State * L, int s) {
 
     if (nargs > s + 1 && is_io_state(L, s+2))
         return push_environment(L, import_modules(env, mnames.size(), mnames.data(), num_threads, to_io_state(L, s+2)));
-    else if (io_state * ios = get_io_state(L))
-        return push_environment(L, import_modules(env, mnames.size(), mnames.data(), num_threads, *ios));
     else
-        return push_environment(L, import_modules(env, mnames.size(), mnames.data(), num_threads, get_tmp_io_state(L)));
+        return push_environment(L, import_modules(env, mnames.size(), mnames.data(), num_threads, get_io_state(L)));
 }
 
 static int import_modules(lua_State * L) {
@@ -1304,7 +1308,7 @@ static void print(io_state * ios, bool reg, char const * msg) {
 /** \brief Thread safe version of print function */
 static int print(lua_State * L, int start, bool reg) {
     lock_guard<mutex> lock(g_print_mutex);
-    io_state * ios = get_io_state(L);
+    io_state * ios = get_io_state_ptr(L);
     int n = lua_gettop(L);
     int i;
     lua_getglobal(L, "tostring");
@@ -1370,7 +1374,7 @@ void set_global_io_state(lua_State * L, io_state & ios) {
 
 set_io_state::set_io_state(lua_State * L, io_state & st) {
     m_state = L;
-    m_prev  = get_io_state(L);
+    m_prev  = get_io_state_ptr(L);
     lua_pushlightuserdata(m_state, static_cast<void *>(&g_set_state_key));
     lua_pushlightuserdata(m_state, &st);
     lua_settable(m_state, LUA_REGISTRYINDEX);
@@ -1389,7 +1393,7 @@ set_io_state::~set_io_state() {
         set_global_options(m_state, m_prev->get_options());
 }
 
-io_state * get_io_state(lua_State * L) {
+io_state * get_io_state_ptr(lua_State * L) {
     lua_pushlightuserdata(L, static_cast<void *>(&g_set_state_key));
     lua_gettable(L, LUA_REGISTRYINDEX);
     if (lua_islightuserdata(L, -1)) {
diff --git a/src/library/kernel_bindings.h b/src/library/kernel_bindings.h
index bafd0a430..568367092 100644
--- a/src/library/kernel_bindings.h
+++ b/src/library/kernel_bindings.h
@@ -74,6 +74,7 @@ public:
    \brief Return the Lean state object associated with the given Lua state.
    Return nullptr is there is none.
 */
-io_state * get_io_state(lua_State * L);
+io_state * get_io_state_ptr(lua_State * L);
+io_state get_io_state(lua_State * L);
 void open_io_state(lua_State * L);
 }
diff --git a/src/library/register_module.h b/src/library/register_module.h
index 9f34d7230..9d407ec54 100644
--- a/src/library/register_module.h
+++ b/src/library/register_module.h
@@ -8,7 +8,7 @@ Author: Leonardo de Moura
 #include "util/script_state.h"
 #include "library/kernel_bindings.h"
 #include "library/resolve_macro.h"
-// #include "library/substitution.h"
+#include "library/coercion.h"
 // #include "library/fo_unify.h"
 // #include "library/hop_match.h"
 // #include "library/placeholder.h"
@@ -17,7 +17,7 @@ namespace lean {
 inline void open_core_module(lua_State * L) {
     open_kernel_module(L);
     open_resolve_macro(L);
-    // open_substitution(L);
+    open_coercion(L);
     // open_fo_unify(L);
     // open_placeholder(L);
     // open_hop_match(L);