diff --git a/src/library/rewrite/rewrite.cpp b/src/library/rewrite/rewrite.cpp
index 16db39870..f97464938 100644
--- a/src/library/rewrite/rewrite.cpp
+++ b/src/library/rewrite/rewrite.cpp
@@ -14,19 +14,7 @@
 #include "library/printer.h"
 #include "library/rewrite/fo_match.h"
 #include "library/rewrite/rewrite.h"
-
-// Term Rewriting
-// ORELSE
-// APP_RW
-// LAMBDA_RW
-// PI_RW
-// LET_RW
-// DEPTH_RW
-// THEOREM2RW
-// TRIVIAL_RW
-// FORALL
-// FAIL
-// FAIL_IF
+#include "library/light_checker.h"
 
 using std::cout;
 using std::endl;
@@ -57,7 +45,7 @@ theorem_rewrite::theorem_rewrite(expr const & type, expr const & body)
     lean_trace("rewrite", tout << "Number of Arg = " << num_args << endl;);
 }
 
-pair<expr, expr> theorem_rewrite::operator()(context & ctx, expr const & v, expr const & ) const throw(rewrite_exception) {
+pair<expr, expr> theorem_rewrite::operator()(context & ctx, expr const & v, environment const & ) const throw(rewrite_exception) {
     lean_trace("rewrite", tout << "Context = " << ctx << endl;);
     lean_trace("rewrite", tout << "Term = " << v << endl;);
     lean_trace("rewrite", tout << "Pattern = " << pattern << endl;);
@@ -97,18 +85,75 @@ pair<expr, expr> theorem_rewrite::operator()(context & ctx, expr const & v, expr
     return make_pair(new_rhs, proof);
 }
 
-pair<expr, expr> orelse_rewrite::operator()(context & ctx, expr const & v, expr const & t) const throw(rewrite_exception) {
+pair<expr, expr> orelse_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
     try {
-        return rewrite1(ctx, v, t);
+        return rw1(ctx, v, env);
     } catch (rewrite_exception & ) {
-        return rewrite2(ctx, v, t);
+        return rw2(ctx, v, env);
     }
 }
 
-pair<expr, expr> then_rewrite::operator()(context & ctx, expr const & v, expr const & t) const throw(rewrite_exception) {
-    pair<expr, expr> result1 = rewrite1(ctx, v, t);
-    pair<expr, expr> result2 = rewrite2(ctx, result1.first, t);
+pair<expr, expr> then_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
+    pair<expr, expr> result1 = rw1(ctx, v, env);
+    pair<expr, expr> result2 = rw2(ctx, result1.first, env);
+    expr const & t = light_checker(env)(v, ctx);
     return make_pair(result2.first,
                      Trans(t, v, result1.first, result2.first, result1.second, result2.second));
 }
+
+pair<expr, expr> app_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
+    if (!is_app(v))
+        throw rewrite_exception();
+
+    unsigned n = num_args(v);
+    for (unsigned i = 0; i < n; i++) {
+        auto result = rw(ctx, arg(v, i), env);
+    }
+
+    // TODO(soonhok)
+    throw rewrite_exception();
+}
+
+pair<expr, expr> lambda_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
+    if (!is_lambda(v))
+        throw rewrite_exception();
+    expr const & domain = abst_domain(v);
+    expr const & body   = abst_body(v);
+
+    auto result_domain = rw(ctx, domain, env);
+    auto result_body   = rw(ctx, body,   env); // TODO(soonhok): add to context!
+
+    // TODO(soonhok)
+    throw rewrite_exception();
+}
+
+pair<expr, expr> pi_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
+    if (!is_pi(v))
+        throw rewrite_exception();
+
+    expr const & domain = abst_domain(v);
+    expr const & body   = abst_body(v);
+
+    auto result_domain = rw(ctx, domain, env);
+    auto result_body   = rw(ctx, body,   env); // TODO(soonhok): add to context!
+
+    // TODO(soonhok)
+    throw rewrite_exception();
+}
+
+pair<expr, expr> let_rewrite::operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception) {
+    if (!is_let(v))
+        throw rewrite_exception();
+
+    expr const & ty    = let_type(v);
+    expr const & value = let_value(v);
+    expr const & body  = let_body(v);
+
+    auto result_ty    = rw(ctx, ty,    env);
+    auto result_value = rw(ctx, value, env);
+    auto result_body  = rw(ctx, body,  env); // TODO(soonhok): add to context!
+
+    // TODO(soonhok)
+    throw rewrite_exception();
+}
 }
diff --git a/src/library/rewrite/rewrite.h b/src/library/rewrite/rewrite.h
index 8f35ca8ac..cb04c5d5d 100644
--- a/src/library/rewrite/rewrite.h
+++ b/src/library/rewrite/rewrite.h
@@ -7,6 +7,18 @@ Author: Soonho Kong
 #pragma once
 #include <utility>
 #include "util/exception.h"
+#include "kernel/environment.h"
+
+// Term Rewriting
+// APP_RW
+// LAMBDA_RW
+// PI_RW
+// LET_RW
+// DEPTH_RW
+// TRIVIAL_RW
+// FORALL
+// FAIL
+// FAIL_IF
 
 namespace lean {
 
@@ -15,7 +27,7 @@ class rewrite_exception : public exception {
 
 class rewrite {
 public:
-    virtual std::pair<expr, expr> operator()(context & ctx, expr const & v, expr const & t) const = 0;
+    virtual std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const = 0;
 };
 
 class theorem_rewrite : public rewrite {
@@ -28,29 +40,66 @@ private:
 
 public:
     theorem_rewrite(expr const & type, expr const & body);
-    std::pair<expr, expr> operator()(context & ctx, expr const & v, expr const & t) const throw(rewrite_exception);
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
 };
 
 class orelse_rewrite : public rewrite {
 private:
-    rewrite const & rewrite1;
-    rewrite const & rewrite2;
+    rewrite const & rw1;
+    rewrite const & rw2;
 public:
-    orelse_rewrite(rewrite const & rw1, rewrite const & rw2) :
-        rewrite1(rw1), rewrite2(rw2) { }
-    std::pair<expr, expr> operator()(context & ctx, expr const & v, expr const & t) const throw(rewrite_exception);
+    orelse_rewrite(rewrite const & rw_1, rewrite const & rw_2) :
+        rw1(rw_1), rw2(rw_2) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
 };
 
 class then_rewrite : public rewrite {
 private:
-    rewrite const & rewrite1;
-    rewrite const & rewrite2;
+    rewrite const & rw1;
+    rewrite const & rw2;
 public:
-    then_rewrite(rewrite const & rw1, rewrite const & rw2) :
-        rewrite1(rw1), rewrite2(rw2) { }
-    std::pair<expr, expr> operator()(context & ctx, expr const & v, expr const & t) const throw(rewrite_exception);
+    then_rewrite(rewrite const & rw_1, rewrite const & rw_2) :
+        rw1(rw_1), rw2(rw_2) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
 };
 
+class app_rewrite : public rewrite {
+private:
+    rewrite const & rw;
+public:
+    app_rewrite(rewrite const & rw_) :
+        rw(rw_) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
+};
+
+class lambda_rewrite : public rewrite {
+private:
+    rewrite const & rw;
+public:
+    lambda_rewrite(rewrite const & rw_) :
+        rw(rw_) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
+};
+
+class pi_rewrite : public rewrite {
+private:
+    rewrite const & rw;
+public:
+    pi_rewrite(rewrite const & rw_) :
+        rw(rw_) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
+};
+
+class let_rewrite : public rewrite {
+private:
+    rewrite const & rw;
+public:
+    let_rewrite(rewrite const & rw_) :
+        rw(rw_) { }
+    std::pair<expr, expr> operator()(context & ctx, expr const & v, environment const & env) const throw(rewrite_exception);
+};
+
+
 class fail_rewrite : public rewrite {
 public:
     std::pair<expr, expr> operator()(context &, expr const &) const throw(rewrite_exception) {
diff --git a/src/tests/library/rewrite/rewrite.cpp b/src/tests/library/rewrite/rewrite.cpp
index 640e7f60a..53b1d0941 100644
--- a/src/tests/library/rewrite/rewrite.cpp
+++ b/src/tests/library/rewrite/rewrite.cpp
@@ -8,7 +8,6 @@ Author: Soonho Kong
 #include "kernel/abstract.h"
 #include "kernel/context.h"
 #include "kernel/expr.h"
-#include "kernel/type_checker.h"
 #include "library/all/all.h"
 #include "library/arith/arith.h"
 #include "library/arith/nat.h"
@@ -44,7 +43,7 @@ static void theorem_rewrite1_tst() {
     // Rewriting
     theorem_rewrite add_comm_thm_rewriter(add_comm_thm_type, add_comm_thm_body);
     context ctx;
-    pair<expr, expr> result = add_comm_thm_rewriter(ctx, a_plus_b, Nat);
+    pair<expr, expr> result = add_comm_thm_rewriter(ctx, a_plus_b, env);
     expr concl = mk_eq(a_plus_b, result.first);
     expr proof = result.second;
 
@@ -75,7 +74,7 @@ static void theorem_rewrite2_tst() {
     // Rewriting
     theorem_rewrite add_id_thm_rewriter(add_id_thm_type, add_id_thm_body);
     context ctx;
-    pair<expr, expr> result = add_id_thm_rewriter(ctx, a_plus_zero, Nat);
+    pair<expr, expr> result = add_id_thm_rewriter(ctx, a_plus_zero, env);
     expr concl = mk_eq(a_plus_zero, result.first);
     expr proof = result.second;
 
@@ -116,7 +115,7 @@ static void then_rewrite1_tst() {
     theorem_rewrite add_id_thm_rewriter(add_id_thm_type, add_id_thm_body);
     then_rewrite    then_rewriter1(add_comm_thm_rewriter, add_id_thm_rewriter);
     context ctx;
-    pair<expr, expr> result = then_rewriter1(ctx, zero_plus_a, Nat);
+    pair<expr, expr> result = then_rewriter1(ctx, zero_plus_a, env);
     expr concl = mk_eq(zero_plus_a, result.first);
     expr proof = result.second;
 
@@ -175,7 +174,7 @@ static void then_rewrite2_tst() {
     then_rewrite    then_rewriter2(then_rewrite(add_assoc_thm_rewriter, add_id_thm_rewriter),
                                    then_rewrite(add_comm_thm_rewriter, add_id_thm_rewriter));
     context ctx;
-    pair<expr, expr> result = then_rewriter2(ctx, zero_plus_a_plus_zero, Nat);
+    pair<expr, expr> result = then_rewriter2(ctx, zero_plus_a_plus_zero, env);
     expr concl = mk_eq(zero_plus_a_plus_zero, result.first);
     expr proof = result.second;
     cout << "Theorem: " << add_assoc_thm_type << " := " << add_assoc_thm_body << endl;
@@ -227,7 +226,7 @@ static void orelse_rewrite1_tst() {
     theorem_rewrite add_comm_thm_rewriter(add_comm_thm_type, add_comm_thm_body);
     orelse_rewrite  add_assoc_or_comm_thm_rewriter(add_assoc_thm_rewriter, add_comm_thm_rewriter);
     context ctx;
-    pair<expr, expr> result = add_assoc_or_comm_thm_rewriter(ctx, a_plus_b, Nat);
+    pair<expr, expr> result = add_assoc_or_comm_thm_rewriter(ctx, a_plus_b, env);
     expr concl = mk_eq(a_plus_b, result.first);
     expr proof = result.second;