diff --git a/src/kernel/instantiate.cpp b/src/kernel/instantiate.cpp
index 3991aefec..a51cbcba7 100644
--- a/src/kernel/instantiate.cpp
+++ b/src/kernel/instantiate.cpp
@@ -121,28 +121,6 @@ expr head_beta_reduce(expr const & t) {
     }
 }
 
-expr beta_reduce(expr t) {
-    bool reduced = false;
-    auto f = [&](expr const & m, unsigned) -> optional<expr> {
-        if (is_head_beta(m)) {
-            reduced = true;
-            return some_expr(head_beta_reduce(m));
-        } else if (is_local(m) || is_metavar(m)) {
-            return some_expr(m); // do not simplify local constants and metavariables types.
-        } else {
-            return none_expr();
-        }
-    };
-    while (true) {
-        reduced = false;
-        expr new_t = replace(t, f);
-        if (!reduced)
-            return new_t;
-        else
-            t = new_t;
-    }
-}
-
 expr instantiate_univ_params(expr const & e, level_param_names const & ps, levels const & ls) {
     if (!has_param_univ(e))
         return e;
diff --git a/src/kernel/instantiate.h b/src/kernel/instantiate.h
index aa4f7e8cf..6047f69bc 100644
--- a/src/kernel/instantiate.h
+++ b/src/kernel/instantiate.h
@@ -24,7 +24,6 @@ expr instantiate_rev(expr const & e, unsigned n, expr const * s);
 expr apply_beta(expr f, unsigned num_args, expr const * args);
 bool is_head_beta(expr const & t);
 expr head_beta_reduce(expr const & t);
-expr beta_reduce(expr t);
 
 /** \brief Instantiate the universe level parameters \c ps occurring in \c e with the levels \c ls.
     \pre length(ps) == length(ls)
diff --git a/src/library/normalize.cpp b/src/library/normalize.cpp
index 7fdc58977..82c2cc8f7 100644
--- a/src/library/normalize.cpp
+++ b/src/library/normalize.cpp
@@ -7,11 +7,13 @@ Author: Leonardo de Moura
 #include <string>
 #include "util/interrupt.h"
 #include "util/name_generator.h"
+#include "kernel/replace_fn.h"
 #include "kernel/type_checker.h"
 #include "kernel/instantiate.h"
 #include "kernel/abstract.h"
 #include "kernel/free_vars.h"
 #include "kernel/inductive/inductive.h"
+#include "library/replace_visitor.h"
 #include "library/reducible.h"
 #include "library/util.h"
 #include "library/scoped_ext.h"
@@ -186,6 +188,42 @@ expr try_eta(expr const & e) {
     }
 }
 
+template<bool Eta, bool Beta>
+class eta_beta_reduce_fn : public replace_visitor {
+public:
+    virtual expr visit_app(expr const & e) {
+        expr e1 = replace_visitor::visit_app(e);
+        if (Beta && is_head_beta(e1)) {
+            return visit(head_beta_reduce(e1));
+        } else {
+            return e1;
+        }
+    }
+
+    virtual expr visit_lambda(expr const & e) {
+        expr e1 = replace_visitor::visit_lambda(e);
+        if (Eta) {
+            while (true) {
+                expr e2 = try_eta(e1);
+                if (is_eqp(e1, e2))
+                    return e1;
+                else
+                    e1 = e2;
+            }
+        } else {
+            return e1;
+        }
+    }
+};
+
+expr beta_reduce(expr t) {
+    return eta_beta_reduce_fn<false, true>()(t);
+}
+
+expr beta_eta_reduce(expr t) {
+    return eta_beta_reduce_fn<true, true>()(t);
+}
+
 class normalize_fn {
     type_checker   &                  m_tc;
     name_generator                    m_ngen;
diff --git a/src/library/normalize.h b/src/library/normalize.h
index cd3f25a46..b428df3fb 100644
--- a/src/library/normalize.h
+++ b/src/library/normalize.h
@@ -61,6 +61,8 @@ environment erase_constructor_hint(environment const & env, name const & n, bool
 optional<unsigned> has_constructor_hint(environment const & env, name const & d);
 
 expr try_eta(expr const & e);
+expr beta_reduce(expr t);
+expr beta_eta_reduce(expr t);
 
 void initialize_normalize();
 void finalize_normalize();
diff --git a/src/library/tactic/rewrite_tactic.cpp b/src/library/tactic/rewrite_tactic.cpp
index d48edd45a..7f2e35dff 100644
--- a/src/library/tactic/rewrite_tactic.cpp
+++ b/src/library/tactic/rewrite_tactic.cpp
@@ -52,10 +52,16 @@ Author: Leonardo de Moura
 #define LEAN_DEFAULT_REWRITER_TRACE true
 #endif
 
+#ifndef LEAN_DEFAULT_REWRITER_BETA_ETA
+#define LEAN_DEFAULT_REWRITER_BETA_ETA true
+#endif
+
+
 namespace lean {
 static name * g_rewriter_max_iterations = nullptr;
 static name * g_rewriter_syntactic      = nullptr;
 static name * g_rewriter_trace          = nullptr;
+static name * g_rewriter_beta_eta       = nullptr;
 
 unsigned get_rewriter_max_iterations(options const & opts) {
     return opts.get_unsigned(*g_rewriter_max_iterations, LEAN_DEFAULT_REWRITER_MAX_ITERATIONS);
@@ -69,6 +75,10 @@ bool get_rewriter_trace(options const & opts) {
     return opts.get_bool(*g_rewriter_trace, LEAN_DEFAULT_REWRITER_TRACE);
 }
 
+bool get_rewriter_beta_eta(options const & opts) {
+    return opts.get_bool(*g_rewriter_beta_eta, LEAN_DEFAULT_REWRITER_BETA_ETA);
+}
+
 class unfold_info {
     list<name> m_names;
     location   m_location;
@@ -568,6 +578,7 @@ class rewrite_fn {
     bool                 m_use_trace;
     bool                 m_keyed;
     unsigned             m_max_iter;
+    bool                 m_beta_eta;
 
     buffer<optional<level>> m_lsubst; // auxiliary buffer for pattern matching
     buffer<optional<expr>>  m_esubst; // auxiliary buffer for pattern matching
@@ -1271,9 +1282,16 @@ class rewrite_fn {
         lean::check_term(m_env, m_g.abstract(H));
     }
 
+    expr apply_beta_eta(expr const & e) {
+        if (m_beta_eta)
+            return beta_eta_reduce(e);
+        else
+            return e;
+    }
+
     bool process_rewrite_hypothesis(expr const & hyp, expr const & orig_elem, expr const & pattern, occurrence const & occ) {
         add_target(hyp, true);
-        expr Pa = mlocal_type(hyp);
+        expr Pa = apply_beta_eta(mlocal_type(hyp));
         bool is_goal = false;
         if (auto it = find_target(Pa, pattern, orig_elem, is_goal)) {
             expr a, Heq, b; // Heq is a proof of a = b
@@ -1326,7 +1344,7 @@ class rewrite_fn {
     }
 
     bool process_rewrite_goal(expr const & orig_elem, expr const & pattern, occurrence const & occ) {
-        expr Pa      = m_g.get_type();
+        expr Pa      = apply_beta_eta(m_g.get_type());
         add_target(Pa, false);
         bool is_goal = true;
         if (auto it = find_target(Pa, pattern, orig_elem, is_goal)) {
@@ -1539,6 +1557,7 @@ public:
         m_subst = m_ps.get_subst();
         m_max_iter  = get_rewriter_max_iterations(ios.get_options());
         m_use_trace = get_rewriter_trace(ios.get_options());
+        m_beta_eta  = get_rewriter_beta_eta(ios.get_options());
     }
 
     proof_state_seq operator()(buffer<expr> const & elems) {
@@ -1594,6 +1613,10 @@ void initialize_rewrite_tactic() {
     g_rewriter_trace          = new name{"rewriter", "trace"};
     register_bool_option(*g_rewriter_trace, LEAN_DEFAULT_REWRITER_TRACE,
                          "(rewriter tactic) if true tactic will generate a trace for rewrite step failures");
+    g_rewriter_beta_eta       = new name{"rewriter", "beta_eta"};
+    register_bool_option(*g_rewriter_beta_eta, LEAN_DEFAULT_REWRITER_BETA_ETA,
+                         "(rewriter tactic) apply beta and eta reduction before rewrite steps");
+
     name rewrite_tac_name{"tactic", "rewrite_tac"};
     g_rewrite_tac           = new expr(Const(rewrite_tac_name));
     g_xrewrite_tac          = new expr(Const(name{"tactic", "xrewrite_tac"}));
diff --git a/src/library/tactic/tactic.cpp b/src/library/tactic/tactic.cpp
index 3812adc44..ace9ce2b7 100644
--- a/src/library/tactic/tactic.cpp
+++ b/src/library/tactic/tactic.cpp
@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "kernel/type_checker.h"
 #include "kernel/for_each_fn.h"
 #include "kernel/replace_fn.h"
+#include "library/normalize.h"
 #include "library/kernel_bindings.h"
 #include "library/tactic/tactic.h"
 #include "library/io_state_stream.h"
diff --git a/src/tests/kernel/instantiate.cpp b/src/tests/kernel/instantiate.cpp
index aebbf5400..71ed92415 100644
--- a/src/tests/kernel/instantiate.cpp
+++ b/src/tests/kernel/instantiate.cpp
@@ -32,7 +32,6 @@ static void tst1() {
     expr F3 = mk_app(Fun(x, mk_app(f, mk_app(Fun(y, y), x), x)), a);
     lean_assert(is_head_beta(F3));
     lean_assert(head_beta_reduce(F3) == mk_app(f, mk_app(Fun(y, y), a), a));
-    lean_assert(beta_reduce(F3) == mk_app(f, a, a));
 }
 
 int main() {
diff --git a/tests/lean/finset_induction_bug.lean.expected.out b/tests/lean/finset_induction_bug.lean.expected.out
index e352f339c..641094896 100644
--- a/tests/lean/finset_induction_bug.lean.expected.out
+++ b/tests/lean/finset_induction_bug.lean.expected.out
@@ -1,5 +1,5 @@
 finset_induction_bug.lean:30:23: error:invalid 'rewrite' tactic, step produced type incorrect term, details: type mismatch at application
-  @subtype.tag (list A) (λ (l : list A), @nodup A l) x nodup_al'
+  @subtype.tag (list A) (@nodup A) x nodup_al'
 term
   nodup_al'
 has type