diff --git a/src/library/tactic/location.h b/src/library/tactic/location.h
index 3c5868e58..7ea4e8cb7 100644
--- a/src/library/tactic/location.h
+++ b/src/library/tactic/location.h
@@ -71,6 +71,8 @@ public:
     static location mk_hypotheses_at(buffer<name> const & hs, buffer<occurrence> const & occs);
     static location mk_at(occurrence const & g_occs, buffer<name> const & hs, buffer<occurrence> const & hs_occs);
 
+    bool is_goal_only() const { return m_kind == GoalOnly; }
+
     optional<occurrence> includes_goal() const;
     optional<occurrence> includes_hypothesis(name const & h) const;
     void get_explicit_hypotheses_names(buffer<name> & r) const;
diff --git a/src/library/tactic/rewrite_tactic.cpp b/src/library/tactic/rewrite_tactic.cpp
index 7466db7f5..c7da2e82c 100644
--- a/src/library/tactic/rewrite_tactic.cpp
+++ b/src/library/tactic/rewrite_tactic.cpp
@@ -5,10 +5,22 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #include <string>
+#include "util/interrupt.h"
+#include "util/list_fn.h"
+#include "kernel/instantiate.h"
+#include "kernel/replace_fn.h"
+#include "kernel/for_each_fn.h"
 #include "library/kernel_serializer.h"
+#include "library/reducible.h"
+#include "library/util.h"
+#include "library/match.h"
+#include "library/projection.h"
+#include "library/generic_exception.h"
 #include "library/tactic/rewrite_tactic.h"
 #include "library/tactic/expr_to_tactic.h"
 
+// #define TRACE_MATCH_PLUGIN
+
 namespace lean {
 class unfold_info {
     name      m_name;
@@ -33,7 +45,9 @@ deserializer & operator>>(deserializer & d, unfold_info & e) {
 }
 
 class rewrite_info {
+public:
     enum multiplicity { Once, AtMostN, ExactlyN, ZeroOrMore, OneOrMore };
+private:
     bool                 m_symm;
     multiplicity         m_multiplicity;
     optional<unsigned>   m_num;
@@ -60,7 +74,7 @@ public:
     }
 
     static rewrite_info mk_one_or_more(bool symm, location const & loc) {
-        return rewrite_info(symm, ZeroOrMore, optional<unsigned>(), loc);
+        return rewrite_info(symm, OneOrMore, optional<unsigned>(), loc);
     }
 
     bool symm() const {
@@ -80,7 +94,7 @@ public:
         return *m_num;
     }
 
-    location get_location() const { return m_location; }
+    location const & get_location() const { return m_location; }
 
     friend serializer & operator<<(serializer & s, rewrite_info const & elem);
     friend deserializer & operator>>(deserializer & d, rewrite_info & e);
@@ -135,6 +149,11 @@ bool is_rewrite_unfold_step(expr const & e) {
     return is_macro(e) && macro_def(e).get_name() == *g_rewrite_unfold_name;
 }
 
+unfold_info const & get_rewrite_unfold_info(expr const & e) {
+    lean_assert(is_rewrite_unfold_step(e));
+    return static_cast<rewrite_unfold_macro_cell const*>(macro_def(e).raw())->get_info();
+}
+
 class rewrite_element_macro_cell : public macro_definition_cell {
     rewrite_info m_info;
 public:
@@ -201,6 +220,11 @@ expr const & get_rewrite_pattern(expr const & e) {
     return macro_arg(e, 1);
 }
 
+rewrite_info const & get_rewrite_info(expr const & e) {
+    lean_assert(is_rewrite_step(e));
+    return static_cast<rewrite_element_macro_cell const*>(macro_def(e).raw())->get_info();
+}
+
 expr mk_rewrite_tactic_expr(buffer<expr> const & elems) {
     lean_assert(std::all_of(elems.begin(), elems.end(), [](expr const & e) {
                 return is_rewrite_step(e) || is_rewrite_unfold_step(e);
@@ -208,16 +232,349 @@ expr mk_rewrite_tactic_expr(buffer<expr> const & elems) {
     return mk_app(*g_rewrite_tac, mk_expr_list(elems.size(), elems.data()));
 }
 
-tactic mk_rewrite_tactic(buffer<expr> const & elems) {
-    // TODO(Leo)
-    std::cout << "rewrite_tactic\n";
-    for (auto const & e : elems) {
-        if (is_rewrite_step(e))
-            std::cout << ">> " << get_rewrite_rule(e) << "\n";
-        else
-            std::cout << ">> unfold\n";
+class rewrite_match_plugin : public match_plugin {
+#ifdef TRACE_MATCH_PLUGIN
+    io_state       m_ios;
+#endif
+    type_checker & m_tc;
+public:
+#ifdef TRACE_MATCH_PLUGIN
+    rewrite_match_plugin(io_state const & ios, type_checker & tc):
+        m_ios(ios), m_tc(tc) {}
+#else
+    rewrite_match_plugin(io_state const &, type_checker & tc):
+        m_tc(tc) {}
+#endif
+
+    bool is_projection_app(expr const & e) const {
+        expr const & f = get_app_fn(e);
+        return is_constant(f) && is_projection(m_tc.env(), const_name(f));
     }
-    return id_tactic();
+
+    virtual bool on_failure(expr const & p, expr const & t, match_context & ctx) const {
+        try {
+            constraint_seq cs;
+            expr p1 = is_projection_app(p) ? p : m_tc.whnf(p, cs);
+            expr t1 = is_projection_app(t) ? t : m_tc.whnf(t, cs);
+            return !cs && (p1 != p || t1 != t) && ctx.match(p1, t1);
+        } catch (exception&) {
+            return false;
+        }
+    }
+
+    virtual lbool pre(expr const & p, expr const & t, match_context & ctx) const {
+        if (!is_app(p) || !is_app(t))
+            return l_undef;
+        expr const & p_fn = get_app_fn(p);
+        if (!is_constant(p_fn))
+            return l_false;
+        expr const & t_fn = get_app_fn(t);
+        if (!is_constant(t_fn))
+            return l_false;
+        if (!ctx.match(p_fn, t_fn))
+            return l_false;
+        projection_info const * info = get_projection_info(m_tc.env(), const_name(p_fn));
+        if (!info || !info->m_inst_implicit)
+            return l_undef; // use default matcher
+        buffer<expr> p_args, t_args;
+        get_app_args(p, p_args);
+        get_app_args(t, t_args);
+        if (p_args.size() != t_args.size())
+            return l_false;
+        for (unsigned i = 0; i < p_args.size(); i++) {
+            if (i == info->m_nparams)
+                continue; // skip structure
+            if (!ctx.match(p_args[i], t_args[i]))
+                return l_false;
+        }
+        return l_true;
+    }
+};
+
+class rewrite_fn {
+    environment          m_env;
+    io_state             m_ios;
+    elaborate_fn         m_elab;
+    proof_state          m_ps;
+    name_generator       m_ngen;
+    type_checker_ptr     m_tc;
+    rewrite_match_plugin m_mplugin;
+    goal                 m_g;
+    substitution         m_subst;
+    expr                 m_expr_loc; // auxiliary expression used for error localization
+
+    buffer<optional<level>> m_lsubst; // auxiliary buffer for pattern matching
+    buffer<optional<expr>>  m_esubst; // auxiliary buffer for pattern matching
+
+    [[ noreturn ]] void throw_rewrite_exception(char const * msg) {
+        throw_generic_exception(msg, m_expr_loc);
+    }
+
+    [[ noreturn ]] void throw_rewrite_exception(sstream const & strm) {
+        throw_generic_exception(strm, m_expr_loc);
+    }
+
+    expr mk_meta(expr const & type) {
+        return m_g.mk_meta(m_ngen.next(), type);
+    }
+
+    void elaborate_elems(buffer<expr> const & elems, buffer<expr> & new_elems) {
+        for (expr const & elem : elems) {
+            if (is_rewrite_unfold_step(elem)) {
+                // nothing to be done
+                new_elems.push_back(elem);
+            } else {
+                expr rule = get_rewrite_rule(elem);
+                auto rcs       = m_elab(m_g, m_ngen.mk_child(), rule, false);
+                rule           = rcs.first;
+                if (has_rewrite_pattern(elem)) {
+                    auto pcs     = m_elab(m_g, m_ngen.mk_child(), get_rewrite_pattern(elem), false);
+                    expr pattern = pcs.first;
+                    // We ignore any constraints generated when elaborating patterns.
+                    // The pattern is just a hint to locate positions where the rule should be applied.
+                    expr new_args[2] = { rule, pattern };
+                    new_elems.push_back(mk_macro(macro_def(elem), 2, new_args));
+                } else {
+                    new_elems.push_back(mk_macro(macro_def(elem), 1, &rule));
+                }
+            }
+        }
+    }
+
+    bool process_unfold_step(expr const & elem) {
+        lean_assert(is_rewrite_unfold_step(elem));
+        // TODO(Leo)
+        return false;
+    }
+
+    // Replace metavariables with special metavariables for the higher-order matcher. This is method is used when
+    // converting an expression into a pattern.
+    expr to_meta_idx(expr const & e) {
+        m_lsubst.clear();
+        m_esubst.clear();
+        name_map<expr>  emap;
+        name_map<level> lmap;
+
+        auto to_meta_idx = [&](level const & l) {
+            return replace(l, [&](level const & l) {
+                    if (!has_meta(l)) {
+                        return some_level(l);
+                    } else if (is_meta(l)) {
+                        if (auto it = lmap.find(meta_id(l))) {
+                            return some_level(*it);
+                        } else {
+                            unsigned next_idx = m_lsubst.size();
+                            level r = mk_idx_meta_univ(next_idx);
+                            m_lsubst.push_back(none_level());
+                            lmap.insert(meta_id(l), r);
+                            return some_level(r);
+                        }
+                    } else {
+                        return none_level();
+                    }
+                });
+        };
+
+        return replace(e, [&](expr const & e, unsigned) {
+                if (!has_metavar(e)) {
+                    return some_expr(e); // done
+                } else if (is_binding(e)) {
+                    throw_rewrite_exception("invalid rewrite tactic, pattern contains binders");
+                } else if (is_meta(e)) {
+                    expr const & fn = get_app_fn(e);
+                    lean_assert(is_metavar(fn));
+                    name const & n  = mlocal_name(fn);
+                    if (auto it = emap.find(n)) {
+                        return some_expr(*it);
+                    } else {
+                        unsigned next_idx = m_esubst.size();
+                        expr r = mk_idx_meta(next_idx, m_tc->infer(e).first);
+                        m_esubst.push_back(none_expr());
+                        emap.insert(n, r);
+                        return some_expr(r);
+                    }
+                } else if (is_constant(e)) {
+                    levels ls = map(const_levels(e), [&](level const & l) { return to_meta_idx(l); });
+                    return some_expr(update_constant(e, ls));
+                } else {
+                    return none_expr();
+                }
+            });
+    }
+
+    // Given the rewrite step \c e, return a pattern to be used to locate the term to be rewritten.
+    expr get_pattern(expr const & e) {
+        lean_assert(is_rewrite_step(e));
+        if (has_rewrite_pattern(e)) {
+            return to_meta_idx(get_rewrite_pattern(e));
+        } else {
+            // Remark: we discard constraints generated producing the pattern.
+            // Patterns are only used to locate positions where the rule should be applied.
+            expr rule      = get_rewrite_rule(e);
+            expr rule_type = m_tc->whnf(m_tc->infer(rule).first).first;
+            while (is_pi(rule_type)) {
+                expr meta  = mk_meta(binding_domain(rule_type));
+                rule_type  = m_tc->whnf(instantiate(binding_body(rule_type), meta)).first;
+            }
+            if (!is_eq(rule_type))
+                throw_rewrite_exception("invalid rewrite tactic, given lemma is not an equality");
+            if (get_rewrite_info(e).symm()) {
+                return to_meta_idx(app_arg(rule_type));
+            } else {
+                return to_meta_idx(app_arg(app_fn(rule_type)));
+            }
+        }
+    }
+
+    // Set m_esubst and m_lsubst elements to none
+    void reset_subst() {
+        for (optional<level> & l : m_lsubst)
+            l = none_level();
+        for (optional<expr> & e : m_esubst)
+            e = none_expr();
+    }
+
+    optional<expr> find_target(expr const & e, expr const & pattern) {
+        optional<expr> found;
+        for_each(e, [&](expr const & t, unsigned) {
+                if (found)
+                    return false; // stop search
+                if (closed(t)) {
+                    lean_assert(std::all_of(m_esubst.begin(), m_esubst.end(), [&](optional<expr> const & e) { return !e; }));
+                    bool assigned = false;
+                    bool r = match(pattern, t, m_lsubst, m_esubst, nullptr, nullptr, &m_mplugin, &assigned);
+                    if (assigned)
+                        reset_subst();
+                    if (r) {
+                        found = t;
+                        return false;
+                    }
+                }
+                return true;
+            });
+        return found;
+    }
+
+    bool process_rewrite_hypothesis(expr const & hyp, expr const & elem, expr const & pattern) {
+        // TODO(Leo)
+        return false;
+    }
+
+    bool process_rewrite_goal(expr const & elem, expr const & pattern) {
+        expr goal_type = m_g.get_type();
+        if (auto it = find_target(goal_type, pattern)) {
+            regular(m_env, m_ios) << "found: " << *it << "\n";
+            // TODO(Leo)
+            return false;
+        } else {
+            return false;
+        }
+    }
+
+    bool process_rewrite_single_step(expr const & elem, expr const & pattern) {
+        check_system("rewrite tactic");
+        rewrite_info const & info = get_rewrite_info(elem);
+        location const & loc      = info.get_location();
+        if (loc.is_goal_only())
+            return process_rewrite_goal(elem, pattern);
+        bool progress = false;
+        buffer<expr> hyps;
+        m_g.get_hyps(hyps);
+        for (expr const & h : hyps) {
+            if (!loc.includes_hypothesis(local_pp_name(h)))
+                continue;
+            if (process_rewrite_hypothesis(h, elem, pattern))
+                progress = true;
+        }
+        if (loc.includes_goal() && process_rewrite_goal(elem, pattern))
+            progress = true;
+        return progress;
+    }
+
+    bool process_rewrite_step(expr const & elem) {
+        lean_assert(is_rewrite_step(elem));
+        expr pattern              = get_pattern(elem);
+        regular(m_env, m_ios) << "pattern: " << pattern << "\n";
+        rewrite_info const & info = get_rewrite_info(elem);
+        unsigned num;
+        switch (info.get_multiplicity()) {
+        case rewrite_info::Once:
+            return process_rewrite_single_step(elem, pattern);
+        case rewrite_info::AtMostN:
+            num = info.num();
+            for (unsigned i = 0; i < num; i++) {
+                if (!process_rewrite_single_step(elem, pattern))
+                    return true;
+            }
+            return true;
+        case rewrite_info::ExactlyN:
+            num = info.num();
+            for (unsigned i = 0; i < num; i++) {
+                if (!process_rewrite_single_step(elem, pattern))
+                    return false;
+            }
+            return true;
+        case rewrite_info::ZeroOrMore:
+            while (true) {
+                if (!process_rewrite_single_step(elem, pattern))
+                    return true;
+            }
+        case rewrite_info::OneOrMore:
+            if (!process_rewrite_single_step(elem, pattern))
+                return false;
+            while (true) {
+                if (!process_rewrite_single_step(elem, pattern))
+                    return true;
+            }
+        }
+        lean_unreachable();
+    }
+
+    // Process the given rewrite element/step. This method destructively update
+    // m_g, m_subst, m_ngen. It returns true if it succeeded and false otherwise.
+    bool process_step(expr const & elem) {
+        if (is_rewrite_unfold_step(elem)) {
+            return process_unfold_step(elem);
+        } else {
+            return process_rewrite_step(elem);
+        }
+    }
+
+public:
+    rewrite_fn(environment const & env, io_state const & ios, elaborate_fn const & elab, proof_state const & ps):
+        m_env(env), m_ios(ios), m_elab(elab), m_ps(ps), m_ngen(ps.get_ngen()),
+        m_tc(mk_type_checker(m_env, m_ngen.mk_child(), ps.relax_main_opaque())),
+        m_mplugin(m_ios, *m_tc) {
+        goals const & gs = m_ps.get_goals();
+        lean_assert(gs);
+        m_g     = head(gs);
+        m_subst = m_ps.get_subst();
+    }
+
+    proof_state_seq operator()(buffer<expr> const & elems) {
+        std::cout << "rewrite_tactic\n";
+        buffer<expr> new_elems;
+        elaborate_elems(elems, new_elems);
+
+        lean_assert(elems.size() == new_elems.size());
+        for (unsigned i = 0; i < new_elems.size(); i++) {
+            flet<expr> set1(m_expr_loc, elems[i]);
+            if (!process_step(new_elems[i])) {
+                return proof_state_seq();
+            }
+        }
+
+        return proof_state_seq(m_ps);
+    }
+};
+
+tactic mk_rewrite_tactic(elaborate_fn const & elab, buffer<expr> const & elems) {
+    return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
+            goals const & gs = s.get_goals();
+            if (empty(gs))
+                return proof_state_seq();
+            return rewrite_fn(env, ios, elab, s)(elems);
+        });
 }
 
 void initialize_rewrite_tactic() {
@@ -246,14 +603,14 @@ void initialize_rewrite_tactic() {
                                     return mk_macro(def, num, args);
                                 });
     register_tac(rewrite_tac_name,
-                 [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
+                 [](type_checker &, elaborate_fn const & elab, expr const & e, pos_info_provider const *) {
                      buffer<expr> args;
                      get_tactic_expr_list_elements(app_arg(e), args, "invalid 'rewrite' tactic, invalid argument");
                      for (expr const & arg : args) {
                          if (!is_rewrite_step(arg) && !is_rewrite_unfold_step(arg))
                              throw expr_to_tactic_exception(e, "invalid 'rewrite' tactic, invalid argument");
                      }
-                     return mk_rewrite_tactic(args);
+                     return mk_rewrite_tactic(elab, args);
                  });
 }
 
diff --git a/src/library/tactic/rewrite_tactic.h b/src/library/tactic/rewrite_tactic.h
index 8d34df631..843e0c5da 100644
--- a/src/library/tactic/rewrite_tactic.h
+++ b/src/library/tactic/rewrite_tactic.h
@@ -21,9 +21,6 @@ bool is_rewrite_step(expr const & e);
 /** \brief Create a rewrite tactic expression, where elems was created using \c mk_rewrite_* procedures. */
 expr mk_rewrite_tactic_expr(buffer<expr> const & elems);
 
-/** \brief Create rewrite tactic that applies the given rewrite elements */
-tactic mk_rewrite_tactic(buffer<expr> const & elems);
-
 void initialize_rewrite_tactic();
 void finalize_rewrite_tactic();
 }