diff --git a/src/frontends/lean/elaborator.cpp b/src/frontends/lean/elaborator.cpp
index 988066a0b..6d1ac55c1 100644
--- a/src/frontends/lean/elaborator.cpp
+++ b/src/frontends/lean/elaborator.cpp
@@ -89,7 +89,7 @@ public:
                         return some_level(*it);
                     } else {
                         level new_p = mk_new_univ_param();
-                        m_subst.d_assign(l, new_p);
+                        m_subst.assign(l, new_p);
                         return some_level(new_p);
                     }
                 }
@@ -307,9 +307,9 @@ class elaborator {
                 substitution subst = next->first.get_subst();
                 buffer<constraint> cs;
                 expr const & mvar = get_app_fn(m_meta);
-                cs.push_back(mk_eq_cnstr(mvar, subst.d_instantiate(mvar), m_jst));
+                cs.push_back(mk_eq_cnstr(mvar, subst.instantiate(mvar), m_jst));
                 for (auto const & mvar : m_mvars_in_meta_type)
-                    cs.push_back(mk_eq_cnstr(mvar, subst.d_instantiate(mvar), m_jst));
+                    cs.push_back(mk_eq_cnstr(mvar, subst.instantiate(mvar), m_jst));
                 return optional<constraints>(to_list(cs.begin(), cs.end()));
             }
             return optional<constraints>();
@@ -414,9 +414,7 @@ public:
         if (!m_accumulated.is_none())
             c = update_justification(c, mk_composite1(c.get_justification(), m_accumulated));
         add_cnstr_core(c);
-        auto ss = unify_simple(m_subst, c);
-        m_subst = ss.second;
-        if (ss.first == unify_status::Failed)
+        if (unify_simple(m_subst, c) == unify_status::Failed)
             throw unifier_exception(c.get_justification(), m_subst);
     }
 
@@ -424,7 +422,7 @@ public:
         \remark We update \c m_accumulated with any justifications used.
     */
     expr instantiate_metavars(expr const & e) {
-        auto e_j = m_subst.d_instantiate_metavars(e);
+        auto e_j = m_subst.instantiate_metavars(e);
         m_accumulated = mk_composite1(m_accumulated, e_j.second);
         return e_j.first;
     }
@@ -538,7 +536,7 @@ public:
         return ::lean::is_class(m_env, cls_name) || !empty(get_tactic_hints(m_env, cls_name));
     }
 
-    static expr instantiate_meta(expr const & meta, substitution const & subst) {
+    static expr instantiate_meta(expr const & meta, substitution & subst) {
         buffer<expr> locals;
         expr mvar = get_app_args(meta, locals);
         mvar = update_mlocal(mvar, subst.instantiate(mlocal_type(mvar)));
@@ -551,7 +549,8 @@ public:
     justification mk_failed_to_synthesize_jst(expr const & m) {
         environment env = m_env;
         return mk_justification(m, [=](formatter const & fmt, substitution const & subst) {
-                expr new_m    = instantiate_meta(m, subst);
+                substitution tmp(subst);
+                expr new_m    = instantiate_meta(m, tmp);
                 expr new_type = type_checker(env).infer(new_m);
                 proof_state ps(goals(goal(new_m, new_type)), substitution(), name_generator("dontcare"));
                 return format({format("failed to synthesize placeholder"), line(), ps.pp(fmt)});
@@ -1065,7 +1064,7 @@ public:
             } else {
                 subst = r->first.get_subst();
                 expr v = subst.instantiate(mvar);
-                subst = subst.assign(mlocal_name(mvar), v);
+                subst.assign(mlocal_name(mvar), v);
                 return true;
             }
         } catch (tactic_exception & ex) {
@@ -1110,12 +1109,13 @@ public:
 
     void display_unassigned_mvars(expr const & e, substitution const & s) {
         if (m_check_unassigned && has_metavar(e)) {
+            substitution tmp_s(s);
             for_each(e, [&](expr const & e, unsigned) {
                     if (!is_metavar(e))
                         return has_metavar(e);
                     if (auto it = m_mvar2meta.find(mlocal_name(e))) {
-                        expr meta      = s.instantiate(*it);
-                        expr meta_type = s.instantiate(type_checker(m_env).infer(meta));
+                        expr meta      = tmp_s.instantiate(*it);
+                        expr meta_type = tmp_s.instantiate(type_checker(m_env).infer(meta));
                         goal g(meta, meta_type);
                         display_unsolved_proof_state(e, proof_state(goals(g), substitution(), m_ngen),
                                                      "don't know how to synthesize it");
@@ -1127,7 +1127,7 @@ public:
 
     /** \brief Apply substitution and solve remaining metavariables using tactics. */
     expr apply(substitution & s, expr const & e, name_set & univ_params, buffer<name> & new_params) {
-        expr r = s.d_instantiate(e);
+        expr r = s.instantiate(e);
         if (has_univ_metavar(r))
             r = univ_metavars_to_params_fn(m_env, m_lls, s, univ_params, new_params)(r);
         r = solve_unassigned_mvars(s, r);
@@ -1158,7 +1158,8 @@ public:
         expr r_v      = visit(v);
         expr r_v_type = infer_type(r_v);
         justification j = mk_justification(v, [=](formatter const & fmt, substitution const & subst) {
-                return pp_def_type_mismatch(fmt, n, subst.instantiate(r_t), subst.instantiate(r_v_type));
+                substitution s(subst);
+                return pp_def_type_mismatch(fmt, n, s.instantiate(r_t), s.instantiate(r_v_type));
             });
         if (!m_tc->is_def_eq(r_v_type, r_t, j)) {
             throw_kernel_exception(m_env, v, [=](formatter const & fmt) { return pp_def_type_mismatch(fmt, n, r_t, r_v_type); });
diff --git a/src/kernel/metavar.cpp b/src/kernel/metavar.cpp
index c1e3efc43..17b6ef0f4 100644
--- a/src/kernel/metavar.cpp
+++ b/src/kernel/metavar.cpp
@@ -50,40 +50,20 @@ optional<level> substitution::get_level(name const & m) const {
     return it ? some_level(*it) : none_level();
 }
 
-void substitution::d_assign(name const & m, expr const & t, justification const & j) {
+void substitution::assign(name const & m, expr const & t, justification const & j) {
     lean_assert(closed(t));
     m_expr_subst.insert(m, t);
     if (!j.is_none())
         m_expr_jsts.insert(m, j);
 }
 
-void substitution::d_assign(name const & m, level const & l, justification const & j) {
+void substitution::assign(name const & m, level const & l, justification const & j) {
     m_level_subst.insert(m, l);
     if (!j.is_none())
         m_level_jsts.insert(m, j);
 }
 
-substitution substitution::assign(name const & m, expr const & t, justification const & j) const {
-    substitution s(*this);
-    s.d_assign(m, t, j);
-    return s;
-}
-
-substitution substitution::assign(name const & m, expr const & t) const {
-    return assign(m, t, justification());
-}
-
-substitution substitution::assign(name const & m, level const & l, justification const & j) const {
-    substitution s(*this);
-    s.d_assign(m, l, j);
-    return s;
-}
-
-substitution substitution::assign(name const & m, level const & l) const {
-    return assign(m, l, justification());
-}
-
-std::pair<level, justification> substitution::d_instantiate_metavars(level const & l, bool use_jst, bool updt) {
+std::pair<level, justification> substitution::instantiate_metavars(level const & l, bool use_jst) {
     if (!has_meta(l))
         return mk_pair(l, justification());
     justification j;
@@ -94,14 +74,13 @@ std::pair<level, justification> substitution::d_instantiate_metavars(level const
             } else if (is_meta(l)) {
                 auto p1 = get_assignment(l);
                 if (p1) {
-                    auto p2 = d_instantiate_metavars(p1->first, use_jst, updt);
+                    auto p2 = instantiate_metavars(p1->first, use_jst);
                     if (use_jst) {
                         justification new_jst = mk_composite1(p1->second, p2.second);
-                        if (updt)
-                            d_assign(meta_id(l), p2.first, new_jst);
+                        assign(meta_id(l), p2.first, new_jst);
                         save_jst(new_jst);
-                    } else if (updt) {
-                        d_assign(meta_id(l), p2.first);
+                    } else {
+                        assign(meta_id(l), p2.first);
                     }
                     return some_level(p2.first);
                 }
@@ -116,13 +95,11 @@ protected:
     substitution & m_subst;
     justification  m_jst;
     bool           m_use_jst;
-    bool           m_update;
-    bool           m_only_expr;
 
     void save_jst(justification const & j) { m_jst = mk_composite1(m_jst, j); }
 
     level visit_level(level const & l) {
-        auto p1 = m_subst.d_instantiate_metavars(l, m_use_jst, m_update);
+        auto p1 = m_subst.instantiate_metavars(l, m_use_jst);
         if (m_use_jst)
             save_jst(p1.second);
         return p1.first;
@@ -133,12 +110,10 @@ protected:
     }
 
     virtual expr visit_sort(expr const & s) {
-        lean_assert(!m_only_expr);
         return update_sort(s, visit_level(sort_level(s)));
     }
 
     virtual expr visit_constant(expr const & c) {
-        lean_assert(!m_only_expr);
         return update_constant(c, visit_levels(const_levels(c)));
     }
 
@@ -151,25 +126,15 @@ protected:
                     save_jst(p1->second);
                 return p1->first;
             } else if (m_use_jst) {
-                if (m_update) {
-                    auto p2 = m_subst.d_instantiate_metavars(p1->first);
-                    justification new_jst = mk_composite1(p1->second, p2.second);
-                    m_subst.d_assign(m_name, p2.first, new_jst);
-                    save_jst(new_jst);
-                    return p2.first;
-                } else {
-                    auto p2 = m_subst.instantiate_metavars(p1->first);
-                    save_jst(mk_composite1(p1->second, p2.second));
-                    return p2.first;
-                }
+                auto p2 = m_subst.instantiate_metavars(p1->first);
+                justification new_jst = mk_composite1(p1->second, p2.second);
+                m_subst.assign(m_name, p2.first, new_jst);
+                save_jst(new_jst);
+                return p2.first;
             } else {
-                if (m_update) {
-                    auto p2 = m_subst.d_instantiate_metavars(p1->first);
-                    m_subst.d_assign(m_name, p2.first, mk_composite1(p1->second, p2.second));
-                    return p2.first;
-                } else {
-                    return m_subst.instantiate(p1->first);
-                }
+                auto p2 = m_subst.instantiate_metavars(p1->first);
+                m_subst.assign(m_name, p2.first, mk_composite1(p1->second, p2.second));
+                return p2.first;
             }
         } else {
             return m;
@@ -194,7 +159,7 @@ protected:
     }
 
     virtual expr visit(expr const & e) {
-        if ((m_only_expr && !has_expr_metavar(e)) || (!m_only_expr && !has_metavar(e))) {
+        if (!has_metavar(e)) {
             return e;
         } else {
             return replace_visitor::visit(e);
@@ -202,57 +167,23 @@ protected:
     }
 
 public:
-    instantiate_metavars_fn(substitution & s, bool use_jst, bool updt, bool only_expr = false):
-        m_subst(s), m_use_jst(use_jst), m_update(updt), m_only_expr(only_expr) {}
+    instantiate_metavars_fn(substitution & s, bool use_jst):
+        m_subst(s), m_use_jst(use_jst) {}
     justification const & get_justification() const { return m_jst; }
 };
 
-std::pair<expr, justification> substitution::instantiate_metavars(expr const & e) const {
-    substitution s(*this);
-    instantiate_metavars_fn fn(s, true, false);
-    expr r = fn(e);
-    return mk_pair(r, fn.get_justification());
-}
-
-std::pair<expr, justification> substitution::d_instantiate_metavars(expr const & e, bool only_expr) {
-    if ((only_expr && !has_expr_metavar(e)) || (!only_expr && !has_metavar(e))) {
+std::pair<expr, justification> substitution::instantiate_metavars(expr const & e) {
+    if (!has_metavar(e)) {
         return mk_pair(e, justification());
     } else {
-        instantiate_metavars_fn fn(*this, true, true, only_expr);
+        instantiate_metavars_fn fn(*this, true);
         expr r = fn(e);
         return mk_pair(r, fn.get_justification());
     }
 }
 
-std::tuple<expr, justification, substitution> substitution::updt_instantiate_metavars(expr const & e) const {
-    substitution s(*this);
-    instantiate_metavars_fn fn(s, true, true);
-    expr r = fn(e);
-    return std::make_tuple(r, fn.get_justification(), s);
-}
-
-std::pair<level, justification> substitution::instantiate_metavars(level const & l) const {
-    substitution s(*this);
-    return s.d_instantiate_metavars(l, true, false);
-}
-
-expr substitution::instantiate_metavars_wo_jst(expr const & e) const {
-    substitution s(*this);
-    return instantiate_metavars_fn(s, false, false)(e);
-}
-
-expr substitution::d_instantiate_metavars_wo_jst(expr const & e) {
-    return instantiate_metavars_fn(*this, false, true)(e);
-}
-
-std::pair<expr, substitution> substitution::updt_instantiate_metavars_wo_jst(expr const & e) const {
-    substitution s(*this);
-    return mk_pair(instantiate_metavars_fn(s, false, true)(e), s);
-}
-
-level substitution::instantiate_metavars_wo_jst(level const & l) const {
-    substitution s(*this);
-    return s.d_instantiate_metavars(l, false, false).first;
+expr substitution::instantiate_metavars_wo_jst(expr const & e) {
+    return instantiate_metavars_fn(*this, false)(e);
 }
 
 bool substitution::occurs_expr(name const & m, expr const & e) const {
diff --git a/src/kernel/metavar.h b/src/kernel/metavar.h
index 92e7fab66..c1663cf06 100644
--- a/src/kernel/metavar.h
+++ b/src/kernel/metavar.h
@@ -24,7 +24,8 @@ class substitution {
     jst_map   m_level_jsts;
 
     friend class instantiate_metavars_fn;
-    std::pair<level, justification> d_instantiate_metavars(level const & l, bool use_jst, bool updt);
+    std::pair<level, justification> instantiate_metavars(level const & l, bool use_jst);
+    expr instantiate_metavars_wo_jst(expr const & e);
 
 public:
     substitution();
@@ -42,27 +43,19 @@ public:
     justification get_expr_jst(name const & m) const { if (auto it = m_expr_jsts.find(m)) return *it; else return justification(); }
     justification get_level_jst(name const & m) const { if (auto it = m_level_jsts.find(m)) return *it; else return justification(); }
 
-    substitution assign(name const & m, expr const & t, justification const & j) const;
-    substitution assign(name const & m, expr const & t) const;
+    void assign(name const & m, expr const & t, justification const & j);
+    void assign(name const & m, expr const & t) { assign(m, t, justification()); }
+    void assign(expr const & m, expr const & t, justification const & j) { assign(mlocal_name(m), t, j); }
+    void assign(expr const & m, expr const & t) { assign(m, t, justification()); }
+    void assign(name const & m, level const & t, justification const & j);
+    void assign(name const & m, level const & t) { assign(m, t, justification ()); }
+    void assign(level const & m, level const & t, justification const & j) { assign(meta_id(m), t, j); }
+    void assign(level const & m, level const & t) { assign(m, t, justification ()); }
 
-    substitution assign(name const & m, level const & t, justification const & j) const;
-    substitution assign(name const & m, level const & t) const;
+    std::pair<expr, justification> instantiate_metavars(expr const & e);
+    std::pair<level, justification> instantiate_metavars(level const & l) { return instantiate_metavars(l, true); }
 
-    void d_assign(name const & m, expr const & t, justification const & j);
-    void d_assign(name const & m, expr const & t) { d_assign(m, t, justification()); }
-    void d_assign(expr const & m, expr const & t, justification const & j) { d_assign(mlocal_name(m), t, j); }
-    void d_assign(expr const & m, expr const & t) { d_assign(m, t, justification()); }
-    void d_assign(name const & m, level const & t, justification const & j);
-    void d_assign(name const & m, level const & t) { d_assign(m, t, justification ()); }
-    void d_assign(level const & m, level const & t, justification const & j) { d_assign(meta_id(m), t, j); }
-    void d_assign(level const & m, level const & t) { d_assign(m, t, justification ()); }
-
-    std::pair<expr, justification> d_instantiate_metavars(expr const & e, bool only_expr = false);
-    expr d_instantiate_metavars_wo_jst(expr const & e);
-    std::pair<level, justification> d_instantiate_metavars(level const & l) { return d_instantiate_metavars(l, true, true); }
-
-    void d_forget_justifications() { m_expr_jsts  = jst_map(); m_level_jsts = jst_map(); }
-    substitution forget_justifications() const { substitution s(*this); s.d_forget_justifications(); return s; }
+    void forget_justifications() { m_expr_jsts  = jst_map(); m_level_jsts = jst_map(); }
 
     template<typename F>
     void for_each_expr(F && fn) const {
@@ -77,45 +70,12 @@ public:
     bool is_assigned(expr const & m) const { lean_assert(is_metavar(m)); return is_expr_assigned(mlocal_name(m)); }
     opt_expr_jst get_assignment(expr const & m) const { lean_assert(is_metavar(m)); return get_expr_assignment(mlocal_name(m)); }
     optional<expr> get_expr(expr const & m) const { lean_assert(is_metavar(m)); return get_expr(mlocal_name(m)); }
-    substitution assign(expr const & m, expr const & t, justification const & j) {
-        lean_assert(is_metavar(m)); return assign(mlocal_name(m), t, j); }
-    substitution assign(expr const & m, expr const & t) const { lean_assert(is_metavar(m)); return assign(mlocal_name(m), t); }
 
     bool is_assigned(level const & m) const { lean_assert(is_meta(m)); return is_level_assigned(meta_id(m)); }
     opt_level_jst get_assignment(level const & m) const { lean_assert(is_meta(m)); return get_level_assignment(meta_id(m)); }
     optional<level> get_level(level const & m) const { lean_assert(is_meta(m)); return get_level(meta_id(m)); }
-    substitution assign(level const & m, level const & l, justification const & j) const {
-        lean_assert(is_meta(m)); return assign(meta_id(m), l, j); }
-    substitution assign(level const & m, level const & l) { lean_assert(is_meta(m)); return assign(meta_id(m), l); }
 
-    /**
-        \brief Instantiate metavariables in \c e assigned in this substitution.
-    */
-    std::pair<expr, justification> instantiate_metavars(expr const & e) const;
-
-    /**
-       \brief Similar to the previous function, but it compress the substitution.
-       By compress, we mean, for any metavariable \c m reachable from \c e,
-       if s[m] = t, and t has asssigned metavariables, then s[m] <- instantiate_metavars(t, s).
-       The updated substitution is returned.
-    */
-    std::tuple<expr, justification, substitution> updt_instantiate_metavars(expr const & e) const;
-
-    /** \brief Instantiate level metavariables in \c l. */
-    std::pair<level, justification> instantiate_metavars(level const & l) const;
-
-    /**
-       \brief Instantiate metavariables in \c e assigned in the substitution \c s,
-       but does not return a justification object for the new expression.
-    */
-    expr instantiate_metavars_wo_jst(expr const & e) const;
-    expr instantiate(expr const & e) const { return instantiate_metavars_wo_jst(e); }
-    expr d_instantiate(expr const & e) { return d_instantiate_metavars_wo_jst(e); }
-
-    std::pair<expr, substitution> updt_instantiate_metavars_wo_jst(expr const & e) const;
-
-    /** \brief Instantiate level metavariables in \c l, but does not return justification object. */
-    level instantiate_metavars_wo_jst(level const & l) const;
+    expr instantiate(expr const & e) { return instantiate_metavars_wo_jst(e); }
 
     /** \brief Return true iff the metavariable \c m occurrs (directly or indirectly) in \c e. */
     bool occurs_expr(name const & m, expr const & e) const;
diff --git a/src/kernel/type_checker.cpp b/src/kernel/type_checker.cpp
index 4011d2ee0..344fd6020 100644
--- a/src/kernel/type_checker.cpp
+++ b/src/kernel/type_checker.cpp
@@ -134,7 +134,7 @@ expr type_checker::ensure_sort_core(expr e, expr const & s) {
         expr r = mk_sort(mk_meta_univ(m_gen.next()));
         justification j = mk_justification(s,
                                            [=](formatter const & fmt, substitution const & subst) {
-                                               return pp_type_expected(fmt, subst.instantiate(s));
+                                               return pp_type_expected(fmt, substitution(subst).instantiate(s));
                                            });
         add_cnstr(mk_eq_cnstr(e, r, j));
         return r;
@@ -153,7 +153,7 @@ expr type_checker::ensure_pi_core(expr e, expr const & s) {
     } else if (is_meta(e)) {
         expr r             = mk_pi_for(m_gen, e);
         justification j    = mk_justification(s, [=](formatter const & fmt, substitution const & subst) {
-                return pp_function_expected(fmt, subst.instantiate(s));
+                return pp_function_expected(fmt, substitution(subst).instantiate(s));
             });
         add_cnstr(mk_eq_cnstr(e, r, j));
         return r;
@@ -182,7 +182,8 @@ app_delayed_justification::app_delayed_justification(expr const & e, expr const
 
 justification mk_app_justification(expr const & e, expr const & d_type, expr const & a_type) {
     auto pp_fn = [=](formatter const & fmt, substitution const & subst) {
-        return pp_app_type_mismatch(fmt, subst.instantiate(e), subst.instantiate(d_type), subst.instantiate(a_type));
+        substitution s(subst);
+        return pp_app_type_mismatch(fmt, s.instantiate(e), s.instantiate(d_type), s.instantiate(a_type));
     };
     return mk_justification(e, pp_fn);
 }
diff --git a/src/library/kernel_bindings.cpp b/src/library/kernel_bindings.cpp
index 337cee4c0..f93f5ba6d 100644
--- a/src/library/kernel_bindings.cpp
+++ b/src/library/kernel_bindings.cpp
@@ -1402,7 +1402,7 @@ static int mk_justification(lua_State * L) {
         environment env = to_environment(L, 2);
         expr e          = to_expr(L, 3);
         justification j = mk_justification(some_expr(e), [=](formatter const & fmt, substitution const & subst) {
-                expr new_e = subst.instantiate(e);
+                expr new_e = substitution(subst).instantiate(e);
                 format r;
                 r += format(s.c_str());
                 r += pp_indent_expr(fmt, new_e);
@@ -1605,28 +1605,29 @@ static int subst_assign(lua_State * L) {
     if (nargs == 3) {
         if (is_expr(L, 3)) {
             if (is_expr(L, 2))
-                return push_substitution(L, to_substitution(L, 1).assign(to_expr(L, 2), to_expr(L, 3)));
+                to_substitution(L, 1).assign(to_expr(L, 2), to_expr(L, 3));
             else
-                return push_substitution(L, to_substitution(L, 1).assign(to_name_ext(L, 2), to_expr(L, 3)));
+                to_substitution(L, 1).assign(to_name_ext(L, 2), to_expr(L, 3));
         } else {
             if (is_level(L, 2))
-                return push_substitution(L, to_substitution(L, 1).assign(to_level(L, 2), to_level(L, 3)));
+                to_substitution(L, 1).assign(to_level(L, 2), to_level(L, 3));
             else
-                return push_substitution(L, to_substitution(L, 1).assign(to_name_ext(L, 2), to_level(L, 3)));
+                to_substitution(L, 1).assign(to_name_ext(L, 2), to_level(L, 3));
         }
     } else {
         if (is_expr(L, 3)) {
             if (is_expr(L, 2))
-                return push_substitution(L, to_substitution(L, 1).assign(to_expr(L, 2), to_expr(L, 3), to_justification(L, 4)));
+                to_substitution(L, 1).assign(to_expr(L, 2), to_expr(L, 3), to_justification(L, 4));
             else
-                return push_substitution(L, to_substitution(L, 1).assign(to_name_ext(L, 2), to_expr(L, 3), to_justification(L, 4)));
+                to_substitution(L, 1).assign(to_name_ext(L, 2), to_expr(L, 3), to_justification(L, 4));
         } else {
             if (is_level(L, 2))
-                return push_substitution(L, to_substitution(L, 1).assign(to_level(L, 2), to_level(L, 3), to_justification(L, 4)));
+                to_substitution(L, 1).assign(to_level(L, 2), to_level(L, 3), to_justification(L, 4));
             else
-                return push_substitution(L, to_substitution(L, 1).assign(to_name_ext(L, 2), to_level(L, 3), to_justification(L, 4)));
+                to_substitution(L, 1).assign(to_name_ext(L, 2), to_level(L, 3), to_justification(L, 4));
         }
     }
+    return 0;
 }
 static int subst_is_assigned(lua_State * L) {
     if (is_expr(L, 2))
@@ -1711,8 +1712,13 @@ static int subst_for_each_level(lua_State * L) {
     return 0;
 }
 
+static int subst_copy(lua_State * L) {
+    return push_substitution(L, substitution(to_substitution(L, 1)));
+}
+
 static const struct luaL_Reg substitution_m[] = {
     {"__gc",                   substitution_gc},
+    {"copy",                   safe_function<subst_copy>},
     {"get_expr",               safe_function<subst_get_expr>},
     {"get_level",              safe_function<subst_get_level>},
     {"assign",                 safe_function<subst_assign>},
diff --git a/src/library/tactic/apply_tactic.cpp b/src/library/tactic/apply_tactic.cpp
index abe10becd..826a7a4a4 100644
--- a/src/library/tactic/apply_tactic.cpp
+++ b/src/library/tactic/apply_tactic.cpp
@@ -123,10 +123,11 @@ proof_state_seq apply_tactic_core(environment const & env, io_state const & ios,
     return map2<proof_state>(substs, [=](substitution const & subst) -> proof_state {
             name_generator new_ngen(ngen);
             type_checker tc(env, new_ngen.mk_child());
-            expr new_e = subst.instantiate(e);
+            substitution new_subst = subst;
+            expr new_e = new_subst.instantiate(e);
             expr new_p = g.abstract(new_e);
             check_has_no_local(new_p, _e, "apply");
-            substitution new_subst = subst.assign(g.get_name(), new_p);
+            new_subst.assign(g.get_name(), new_p);
             goals new_gs = tail_gs;
             if (add_subgoals) {
                 buffer<expr> metas;
@@ -138,7 +139,7 @@ proof_state_seq apply_tactic_core(environment const & env, io_state const & ios,
                 unsigned i = metas.size();
                 while (i > 0) {
                     --i;
-                    new_gs = cons(goal(metas[i], subst.instantiate(tc.infer(metas[i]))), new_gs);
+                    new_gs = cons(goal(metas[i], new_subst.instantiate(tc.infer(metas[i]))), new_gs);
                 }
             }
             return proof_state(new_gs, new_subst, new_ngen);
@@ -184,9 +185,10 @@ expr refresh_univ_metavars(expr const & e, name_generator & ngen) {
 tactic apply_tactic(expr const & e, bool refresh_univ_mvars) {
     return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
             if (refresh_univ_mvars) {
-                name_generator ngen = s.get_ngen();
-                expr new_e = refresh_univ_metavars(s.get_subst().instantiate(e), ngen);
-                proof_state new_s(s, ngen);
+                name_generator ngen    = s.get_ngen();
+                substitution new_subst = s.get_subst();
+                expr new_e = refresh_univ_metavars(new_subst.instantiate(e), ngen);
+                proof_state new_s(s.get_goals(), new_subst, ngen);
                 return apply_tactic_core(env, ios, new_s, new_e, true, true);
             } else {
                 return apply_tactic_core(env, ios, s, e, true, true);
diff --git a/src/library/tactic/tactic.cpp b/src/library/tactic/tactic.cpp
index fb70d7a60..192fa3ec8 100644
--- a/src/library/tactic/tactic.cpp
+++ b/src/library/tactic/tactic.cpp
@@ -227,7 +227,7 @@ tactic assumption_tactic() {
                         }
                     }
                     if (h) {
-                        subst  = subst.assign(g.get_mvar(), g.abstract(*h), justification());
+                        subst.assign(g.get_mvar(), g.abstract(*h), justification());
                         solved = true;
                         return optional<goal>();
                     } else {
@@ -253,8 +253,8 @@ tactic exact_tactic(expr const & _e) {
             if (tc.is_def_eq(e_t, t) && !tc.next_cnstr()) {
                 expr new_p = g.abstract(e);
                 check_has_no_local(new_p, _e, "exact");
-                substitution new_subst = subst.assign(g.get_name(), new_p);
-                return some(proof_state(s, tail(gs), new_subst));
+                subst.assign(g.get_name(), new_p);
+                return some(proof_state(s, tail(gs), subst));
             } else {
                 return none_proof_state();
             }
diff --git a/src/library/unifier.cpp b/src/library/unifier.cpp
index 6601f6252..881a9badf 100644
--- a/src/library/unifier.cpp
+++ b/src/library/unifier.cpp
@@ -110,36 +110,36 @@ expr lambda_abstract_locals(expr const & e, buffer<expr> const & locals) {
     return v;
 }
 
-static std::pair<unify_status, substitution> unify_simple_core(substitution const & s, expr const & lhs, expr const & rhs,
-                                                               justification const & j) {
+unify_status unify_simple_core(substitution & s, expr const & lhs, expr const & rhs, justification const & j) {
     lean_assert(is_meta(lhs));
     buffer<expr> args;
     auto m = is_simple_meta(lhs, args);
     if (!m || is_meta(rhs)) {
-        return mk_pair(unify_status::Unsupported, s);
+        return unify_status::Unsupported;
     } else {
         switch (occurs_context_check(s, rhs, *m, args)) {
-        case l_false: return mk_pair(unify_status::Failed, s);
-        case l_undef: mk_pair(unify_status::Unsupported, s);
+        case l_false: return unify_status::Failed;
+        case l_undef: return unify_status::Unsupported;
         case l_true: {
             expr v = lambda_abstract_locals(rhs, args);
-            return mk_pair(unify_status::Solved, s.assign(mlocal_name(*m), v, j));
+            s.assign(mlocal_name(*m), v, j);
+            return unify_status::Solved;
         }}
     }
     lean_unreachable(); // LCOV_EXCL_LINE
 }
 
-std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j) {
+unify_status unify_simple(substitution & s, expr const & lhs, expr const & rhs, justification const & j) {
     if (lhs == rhs)
-        return mk_pair(unify_status::Solved, s);
+        return unify_status::Solved;
     else if (!has_metavar(lhs) && !has_metavar(rhs))
-        return mk_pair(unify_status::Failed, s);
+        return unify_status::Failed;
     else if (is_meta(lhs))
         return unify_simple_core(s, lhs, rhs, j);
     else if (is_meta(rhs))
         return unify_simple_core(s, rhs, lhs, j);
     else
-        return mk_pair(unify_status::Unsupported, s);
+        return unify_status::Unsupported;
 }
 
 // Return true if m occurs in e
@@ -158,23 +158,24 @@ bool occurs_meta(level const & m, level const & e) {
     return contains;
 }
 
-std::pair<unify_status, substitution> unify_simple_core(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
+unify_status unify_simple_core(substitution & s, level const & lhs, level const & rhs, justification const & j) {
     lean_assert(is_meta(lhs));
     bool contains = occurs_meta(lhs, rhs);
     if (contains) {
         if (is_succ(rhs))
-            return mk_pair(unify_status::Failed, s);
+            return unify_status::Failed;
         else
-            return mk_pair(unify_status::Unsupported, s);
+            return unify_status::Unsupported;
     }
-    return mk_pair(unify_status::Solved, s.assign(meta_id(lhs), rhs, j));
+    s.assign(meta_id(lhs), rhs, j);
+    return unify_status::Solved;
 }
 
-std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
+unify_status unify_simple(substitution & s, level const & lhs, level const & rhs, justification const & j) {
     if (lhs == rhs)
-        return mk_pair(unify_status::Solved, s);
+        return unify_status::Solved;
     else if (!has_meta(lhs) && !has_meta(rhs))
-        return mk_pair(unify_status::Failed, s);
+        return unify_status::Failed;
     else if (is_meta(lhs))
         return unify_simple_core(s, lhs, rhs, j);
     else if (is_meta(rhs))
@@ -182,16 +183,16 @@ std::pair<unify_status, substitution> unify_simple(substitution const & s, level
     else if (is_succ(lhs) && is_succ(rhs))
         return unify_simple(s, succ_of(lhs), succ_of(rhs), j);
     else
-        return mk_pair(unify_status::Unsupported, s);
+        return unify_status::Unsupported;
 }
 
-std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c) {
+unify_status unify_simple(substitution & s, constraint const & c) {
     if (is_eq_cnstr(c))
         return unify_simple(s, cnstr_lhs_expr(c), cnstr_rhs_expr(c), c.get_justification());
     else if (is_level_eq_cnstr(c))
         return unify_simple(s, cnstr_lhs_level(c), cnstr_rhs_level(c), c.get_justification());
     else
-        return mk_pair(unify_status::Unsupported, s);
+        return unify_status::Unsupported;
 }
 
 static constraint g_dont_care_cnstr = mk_eq_cnstr(expr(), expr(), justification());
@@ -421,7 +422,7 @@ struct unifier_fn {
     */
     bool assign(expr const & m, expr const & v, justification const & j) {
         lean_assert(is_metavar(m));
-        m_subst.d_assign(m, v, j);
+        m_subst.assign(m, v, j);
         expr m_type = mlocal_type(m);
         expr v_type;
         try {
@@ -433,7 +434,8 @@ struct unifier_fn {
         if (in_conflict())
             return false;
         justification j1 = mk_justification(m, [=](formatter const & fmt, substitution const & subst) {
-                return pp_type_mismatch(fmt, subst.instantiate(m_type), subst.instantiate(v_type));
+                substitution s(subst);
+                return pp_type_mismatch(fmt, s.instantiate(m_type), s.instantiate(v_type));
             });
         if (!is_def_eq(m_type, v_type, mk_composite1(j1, j)))
             return false;
@@ -456,7 +458,7 @@ struct unifier_fn {
     */
     bool assign(level const & m, level const & v, justification const & j) {
         lean_assert(is_meta(m));
-        m_subst.d_assign(m, v, j);
+        m_subst.assign(m, v, j);
         return true;
     }
 
@@ -507,8 +509,8 @@ struct unifier_fn {
 
     std::pair<constraint, bool> instantiate_metavars(constraint const & c) {
         if (is_eq_cnstr(c)) {
-            auto lhs_jst = m_subst.d_instantiate_metavars(cnstr_lhs_expr(c));
-            auto rhs_jst = m_subst.d_instantiate_metavars(cnstr_rhs_expr(c));
+            auto lhs_jst = m_subst.instantiate_metavars(cnstr_lhs_expr(c));
+            auto rhs_jst = m_subst.instantiate_metavars(cnstr_rhs_expr(c));
             expr lhs = lhs_jst.first;
             expr rhs = rhs_jst.first;
             if (lhs != cnstr_lhs_expr(c) || rhs != cnstr_rhs_expr(c)) {
@@ -517,8 +519,8 @@ struct unifier_fn {
                                true);
             }
         } else if (is_level_eq_cnstr(c)) {
-            auto lhs_jst = m_subst.d_instantiate_metavars(cnstr_lhs_level(c));
-            auto rhs_jst = m_subst.d_instantiate_metavars(cnstr_rhs_level(c));
+            auto lhs_jst = m_subst.instantiate_metavars(cnstr_lhs_level(c));
+            auto rhs_jst = m_subst.instantiate_metavars(cnstr_rhs_level(c));
             level lhs = lhs_jst.first;
             level rhs = rhs_jst.first;
             if (lhs != cnstr_lhs_level(c) || rhs != cnstr_rhs_level(c)) {
@@ -839,7 +841,7 @@ struct unifier_fn {
             set_conflict(c.get_justification());
             return false;
         }
-        auto m_type_jst             = m_subst.d_instantiate_metavars(m_type);
+        auto m_type_jst             = m_subst.instantiate_metavars(m_type);
         lazy_list<constraints> alts = fn(m, m_type_jst.first, m_subst, m_ngen.mk_child());
         return process_lazy_constraints(alts, mk_composite1(c.get_justification(), m_type_jst.second));
     }
@@ -1377,7 +1379,9 @@ struct unifier_fn {
         }
         lean_assert(!in_conflict());
         lean_assert(m_cnstrs.empty());
-        return optional<substitution>(m_subst.forget_justifications());
+        substitution s = m_subst;
+        s.forget_justifications();
+        return optional<substitution>(s);
     }
 };
 
@@ -1409,8 +1413,8 @@ lazy_list<substitution> unify(environment const & env,  unsigned num_cs, constra
 lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen, substitution const & s,
                               unsigned max_steps) {
     substitution new_s = s;
-    expr _lhs = new_s.d_instantiate(lhs);
-    expr _rhs = new_s.d_instantiate(rhs);
+    expr _lhs = new_s.instantiate(lhs);
+    expr _rhs = new_s.instantiate(rhs);
     auto u = std::make_shared<unifier_fn>(env, 0, nullptr, ngen, new_s, false, max_steps);
     if (!u->m_tc->is_def_eq(_lhs, _rhs))
         return lazy_list<substitution>();
@@ -1425,7 +1429,7 @@ lazy_list<substitution> unify(environment const & env, expr const & lhs, expr co
 
 static int unify_simple(lua_State * L) {
     int nargs = lua_gettop(L);
-    std::pair<unify_status, substitution> r;
+    unify_status r;
     if (nargs == 2)
         r = unify_simple(to_substitution(L, 1), to_constraint(L, 2));
     else if (nargs == 3 && is_expr(L, 2))
@@ -1436,9 +1440,7 @@ static int unify_simple(lua_State * L) {
         r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), to_justification(L, 4));
     else
         r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), to_justification(L, 4));
-    push_integer(L, static_cast<unsigned>(r.first));
-    push_substitution(L, r.second);
-    return 2;
+    return push_integer(L, static_cast<unsigned>(r));
 }
 
 typedef lazy_list<substitution> substitution_seq;
diff --git a/src/library/unifier.h b/src/library/unifier.h
index 935e0b4ea..26e09f3e9 100644
--- a/src/library/unifier.h
+++ b/src/library/unifier.h
@@ -32,9 +32,9 @@ enum class unify_status { Solved, Failed, Unsupported };
 
     This function assumes that all assigned metavariables have been substituted.
 */
-std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j);
-std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j);
-std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c);
+unify_status unify_simple(substitution & s, expr const & lhs, expr const & rhs, justification const & j);
+unify_status unify_simple(substitution & s, level const & lhs, level const & rhs, justification const & j);
+unify_status unify_simple(substitution & s, constraint const & c);
 
 lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
                               bool use_exception = true, unsigned max_steps = LEAN_DEFAULT_UNIFIER_MAX_STEPS);
diff --git a/src/tests/kernel/metavar.cpp b/src/tests/kernel/metavar.cpp
index c39c6998e..9d92b409e 100644
--- a/src/tests/kernel/metavar.cpp
+++ b/src/tests/kernel/metavar.cpp
@@ -75,7 +75,7 @@ static void tst1() {
     lean_assert(m1 != m2);
     expr f = Const("f");
     expr a = Const("a");
-    subst = subst.assign(m1, f(a));
+    subst.assign(m1, f(a));
     lean_assert(subst.is_assigned(m1));
     lean_assert(!subst.is_assigned(m2));
     lean_assert(*subst.get_expr(m1) == f(a));
@@ -91,8 +91,8 @@ static void tst2() {
     expr f = Const("f");
     expr g = Const("g");
     expr a = Const("a");
-    s = s.assign(m1, f(m2), mk_assumption_justification(1));
-    s = s.assign(m2, g(a),  mk_assumption_justification(2));
+    s.assign(m1, f(m2), mk_assumption_justification(1));
+    s.assign(m2, g(a),  mk_assumption_justification(2));
     lean_assert(check_assumptions(s.get_assignment(m1)->second, {1}));
     lean_assert(s.occurs(m1, f(m1)));
     lean_assert(s.occurs(m2, f(m1)));
@@ -102,22 +102,8 @@ static void tst2() {
     std::cout << s << "\n";
     auto p1 = s.instantiate_metavars(g(m1));
     check_assumptions(p1.second, {1, 2});
-    lean_assert(check_assumptions(s.get_assignment(m1)->second, {1}));
-    lean_assert(p1.first == g(f(g(a))));
-    auto ts = s.updt_instantiate_metavars(g(m1, m3));
-    s = std::get<2>(ts);
-    check_assumptions(std::get<1>(ts), {1, 2});
-    std::cout << std::get<0>(ts) << "\n";
-    std::cout << s << "\n";
     lean_assert(check_assumptions(s.get_assignment(m1)->second, {1, 2}));
-    lean_assert(std::get<0>(ts) == g(f(g(a)), m3));
-    s = s.assign(m3, f(m1, m2), mk_assumption_justification(3));
-    auto p3 = s.instantiate_metavars(g(m1, m3));
-    lean_assert(check_assumptions(p3.second, {1, 2, 3}));
-    std::cout << p3.first << "\n";
-    std::cout << p3.second << "\n";
-    std::cout << s << "\n";
-    lean_assert_eq(p3.first, g(f(g(a)), f(f(g(a)), g(a))));
+    lean_assert(p1.first == g(f(g(a))));
 }
 
 static void tst3() {
@@ -129,7 +115,7 @@ static void tst3() {
     expr b  = Const("b");
     expr x  = Local("x", Prop);
     expr y  = Local("y", Prop);
-    s = s.assign(m1, Fun({x, y}, f(y, x)));
+    s.assign(m1, Fun({x, y}, f(y, x)));
     lean_assert_eq(s.instantiate_metavars(m1(a, b, g(a))).first, f(b, a, g(a)));
     lean_assert_eq(s.instantiate_metavars(m1(a)).first, Fun(y, f(y, a)));
     lean_assert_eq(s.instantiate_metavars(m1(a, b)).first, f(b, a));
@@ -150,10 +136,10 @@ static void tst4() {
     expr T2 = mk_sort(u);
     expr t  = f(T1, T2, m1, m2);
     lean_assert(s.instantiate_metavars(t).first == t);
-    s = s.assign(m1, a, justification());
-    s = s.assign(m2, m3, justification());
+    s.assign(m1, a, justification());
+    s.assign(m2, m3, justification());
     lean_assert(s.instantiate_metavars(t).first == f(T1, T2, a, m3));
-    s = s.assign(l1, level(), justification());
+    s.assign(l1, level(), justification());
     lean_assert(s.instantiate_metavars(t).first == f(Prop, T2, a, m3));
 }
 
diff --git a/tests/lua/jst1.lua b/tests/lua/jst1.lua
index 34de22934..271ee22e3 100644
--- a/tests/lua/jst1.lua
+++ b/tests/lua/jst1.lua
@@ -12,7 +12,7 @@ local m  = mk_metavar("m", Prop)
 local j2 = justification("expresion must be a Proposition", env, g(m))
 print(j2:pp())
 local s  = substitution()
-s = s:assign(m, f(a))
+s:assign(m, f(a))
 print(j2:pp(s))
 local j3 = assumption_justification(1)
 assert(not j2:depends_on(1))
diff --git a/tests/lua/subst1.lua b/tests/lua/subst1.lua
index 1826c6a26..b450ad372 100644
--- a/tests/lua/subst1.lua
+++ b/tests/lua/subst1.lua
@@ -7,22 +7,22 @@ local f = Const("f")
 local g = Const("g")
 local a = Const("a")
 local t = f(f(a))
-s = s:assign(m, t)
+s:assign(m, t)
 assert(s:is_assigned(m))
 assert(s:is_expr_assigned("m"))
 assert(not s:is_level_assigned("m"))
 assert(s:instantiate(g(m)) == g(t))
-s = s:assign("m", a)
+s:assign("m", a)
 assert(s:instantiate(g(m)) == g(a))
 local l = mk_level_one()
 local u = mk_meta_univ("u")
-s = s:assign(u, l)
+s:assign(u, l)
 assert(s:is_assigned(u))
 assert(s:is_level_assigned("u"))
 assert(not s:is_expr_assigned("u"))
 assert(s:get_expr("m") == a)
 local m2 = mk_metavar("m2", Prop)
-s = s:assign(m2, f(m))
+s:assign(m2, f(m))
 print(s:get_expr("m2"))
 assert(s:occurs(m, f(m2)))
 assert(s:occurs_expr("m", f(m2)))
diff --git a/tests/lua/unify1.lua b/tests/lua/unify1.lua
index cad9e61fd..f202315ee 100644
--- a/tests/lua/unify1.lua
+++ b/tests/lua/unify1.lua
@@ -1,6 +1,7 @@
 function test_unify_simple(lhs, rhs, expected)
    print(tostring(lhs) .. " =?= " .. tostring(rhs) .. ", expected: " .. tostring(expected))
-   r, s = unify_simple(substitution(), lhs, rhs, justification())
+   s = substitution()
+   r = unify_simple(s, lhs, rhs, justification())
    if r == unify_status.Solved then
       s:for_each_expr(function(n, v, j)
                          print("  " .. tostring(n) .. " := " .. tostring(v))