diff --git a/hott/algebra/precategory/yoneda.hlean b/hott/algebra/precategory/yoneda.hlean
index 87e1becb6..94f76e3cf 100644
--- a/hott/algebra/precategory/yoneda.hlean
+++ b/hott/algebra/precategory/yoneda.hlean
@@ -151,6 +151,10 @@ namespace functor
   --     → F₁ = F₂ :=
   -- functor.rec_on F₁ (λO₁ H₁ id₁ comp₁, functor.rec_on F₂ (λO₂ H₂ id₂ comp₂ p, !functor_eq_mk'1))
 
+
+  set_option pp.full_names true
+  open tactic
+  print raw id
   --set_option pp.notation false
   definition functor_uncurry_functor_curry : functor_uncurry (functor_curry F) = F :=
   functor_eq_mk (λp, ap (to_fun_ob F) !prod.eta)
diff --git a/hott/init/tactic.hlean b/hott/init/tactic.hlean
index dbab32fee..3313e5af2 100644
--- a/hott/init/tactic.hlean
+++ b/hott/init/tactic.hlean
@@ -63,37 +63,29 @@ opaque definition revert     (e : expr)   : tactic := builtin
 opaque definition unfold     (e : expr)   : tactic := builtin
 opaque definition exact      (e : expr)   : tactic := builtin
 opaque definition trace      (s : string) : tactic := builtin
-opaque definition inversion  (id : expr)  : tactic := builtin
-
-notation a `↦` b:max := rename a b
 
 inductive expr_list : Type :=
 | nil  : expr_list
 | cons : expr → expr_list → expr_list
 
+-- auxiliary type used to mark optional list of arguments
+definition opt_expr_list := expr_list
+
 -- rewrite_tac is just a marker for the builtin 'rewrite' notation
 -- used to create instances of this tactic.
 opaque definition rewrite_tac (e : expr_list)  : tactic := builtin
 
-opaque definition inversion_with  (id : expr) (ids : expr_list) : tactic := builtin
-notation `cases` a:max := inversion a
-notation `cases` a:max `with` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := inversion_with a l
+opaque definition cases (id : expr) (ids : opt_expr_list) : tactic := builtin
 
-opaque definition intro_lst (ids : expr_list) : tactic := builtin
-notation `intros`   := intro_lst expr_list.nil
-notation `intros` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := intro_lst l
+opaque definition intros (ids : opt_expr_list) : tactic := builtin
 
-opaque definition generalize_lst (es : expr_list) : tactic := builtin
-notation `generalizes` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := generalize_lst l
+opaque definition generalizes (es : expr_list) : tactic := builtin
 
-opaque definition clear_lst  (ids : expr_list) : tactic := builtin
-notation `clears` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := clear_lst l
+opaque definition clears (ids : expr_list) : tactic := builtin
 
-opaque definition revert_lst (ids : expr_list) : tactic := builtin
-notation `reverts` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := revert_lst l
+opaque definition reverts (ids : expr_list) : tactic := builtin
 
-opaque definition change_goal (e : expr) : tactic := builtin
-notation `change` e := change_goal e
+opaque definition change (e : expr) : tactic := builtin
 
 opaque definition assert_hypothesis (id : expr) (e : expr) : tactic := builtin
 
@@ -104,7 +96,7 @@ definition try         (t : tactic) : tactic := [t | id]
 definition repeat1     (t : tactic) : tactic := t ; repeat t
 definition focus       (t : tactic) : tactic := focus_at t 0
 definition determ      (t : tactic) : tactic := at_most t 1
-
+definition trivial                  : tactic := [ apply eq.refl | assumption ]
 definition do (n : num) (t : tactic) : tactic :=
 nat.rec id (λn t', (t;t')) (nat.of_num n)
 
diff --git a/library/init/tactic.lean b/library/init/tactic.lean
index 4bff9d91b..19e70190b 100644
--- a/library/init/tactic.lean
+++ b/library/init/tactic.lean
@@ -62,37 +62,29 @@ opaque definition revert     (e : expr)   : tactic := builtin
 opaque definition unfold     (e : expr)   : tactic := builtin
 opaque definition exact      (e : expr)   : tactic := builtin
 opaque definition trace      (s : string) : tactic := builtin
-opaque definition inversion  (id : expr)  : tactic := builtin
-
-notation a `↦` b:max := rename a b
 
 inductive expr_list : Type :=
 | nil  : expr_list
 | cons : expr → expr_list → expr_list
 
+-- auxiliary type used to mark optional list of arguments
+definition opt_expr_list := expr_list
+
 -- rewrite_tac is just a marker for the builtin 'rewrite' notation
 -- used to create instances of this tactic.
 opaque definition rewrite_tac (e : expr_list) : tactic := builtin
 
-opaque definition inversion_with  (id : expr) (ids : expr_list) : tactic := builtin
-notation `cases` a:max := inversion a
-notation `cases` a:max `with` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := inversion_with a l
+opaque definition cases (id : expr) (ids : opt_expr_list) : tactic := builtin
 
-opaque definition intro_lst (ids : expr_list) : tactic := builtin
-notation `intros`   := intro_lst expr_list.nil
-notation `intros` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := intro_lst l
+opaque definition intros (ids : opt_expr_list) : tactic := builtin
 
-opaque definition generalize_lst (es : expr_list) : tactic := builtin
-notation `generalizes` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := generalize_lst l
+opaque definition generalizes (es : expr_list) : tactic := builtin
 
-opaque definition clear_lst  (ids : expr_list) : tactic := builtin
-notation `clears` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := clear_lst l
+opaque definition clears  (ids : expr_list) : tactic := builtin
 
-opaque definition revert_lst (ids : expr_list) : tactic := builtin
-notation `reverts` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := revert_lst l
+opaque definition reverts (ids : expr_list) : tactic := builtin
 
-opaque definition change_goal (e : expr) : tactic := builtin
-notation `change` e := change_goal e
+opaque definition change (e : expr) : tactic := builtin
 
 opaque definition assert_hypothesis (id : expr) (e : expr) : tactic := builtin
 
@@ -103,7 +95,7 @@ definition try         (t : tactic) : tactic := [t | id]
 definition repeat1     (t : tactic) : tactic := t ; repeat t
 definition focus       (t : tactic) : tactic := focus_at t 0
 definition determ      (t : tactic) : tactic := at_most t 1
-
+definition trivial                  : tactic := [ apply eq.refl | apply true.intro | assumption ]
 definition do (n : num) (t : tactic) : tactic :=
 nat.rec id (λn t', (t;t')) (nat.of_num n)
 
diff --git a/library/logic/axioms/prop_complete.lean b/library/logic/axioms/prop_complete.lean
index 7c2b9d55e..cce9392c9 100644
--- a/library/logic/axioms/prop_complete.lean
+++ b/library/logic/axioms/prop_complete.lean
@@ -12,13 +12,13 @@ axiom prop_complete (a : Prop) : a = true ∨ a = false
 
 definition eq_true_or_eq_false := prop_complete
 
-theorem cases (P : Prop → Prop) (H1 : P true) (H2 : P false) (a : Prop) : P a :=
+theorem cases_true_false (P : Prop → Prop) (H1 : P true) (H2 : P false) (a : Prop) : P a :=
 or.elim (prop_complete a)
   (assume Ht : a = true,  Ht⁻¹ ▸ H1)
   (assume Hf : a = false, Hf⁻¹ ▸ H2)
 
 theorem cases_on (a : Prop) {P : Prop → Prop} (H1 : P true) (H2 : P false) : P a :=
-cases P H1 H2 a
+cases_true_false P H1 H2 a
 
 -- this supercedes the em in decidable
 theorem em (a : Prop) : a ∨ ¬a :=
@@ -37,7 +37,7 @@ by_cases
   (assume H1 : ¬p, false.rec _ (H H1))
 
 theorem eq_false_or_eq_true (a : Prop) : a = false ∨ a = true :=
-cases (λ x, x = false ∨ x = true)
+cases_true_false (λ x, x = false ∨ x = true)
   (or.inr rfl)
   (or.inl rfl)
   a
diff --git a/src/frontends/lean/builtin_exprs.cpp b/src/frontends/lean/builtin_exprs.cpp
index b76f8acaa..fec2f7ceb 100644
--- a/src/frontends/lean/builtin_exprs.cpp
+++ b/src/frontends/lean/builtin_exprs.cpp
@@ -124,34 +124,19 @@ static expr parse_placeholder(parser & p, unsigned, expr const *, pos_info const
     return p.save_pos(mk_explicit_expr_placeholder(), pos);
 }
 
-static environment open_tactic_namespace(parser & p) {
-    if (!is_tactic_namespace_open(p.env())) {
-        environment env = using_namespace(p.env(), p.ios(), get_tactic_name());
-        env = add_aliases(env, get_tactic_name(), name());
-        return env;
-    } else {
-        return p.env();
-    }
-}
-
 static expr parse_by(parser & p, unsigned, expr const *, pos_info const & pos) {
-    environment env = open_tactic_namespace(p);
     parser::undef_id_to_local_scope scope(p);
-    parser::local_scope scope2(p, env);
-    parser::undef_id_to_local_scope scope1(p);
     p.next();
-    expr t = p.parse_expr();
+    expr t = p.parse_tactic();
     return p.mk_by(t, pos);
 }
 
 static expr parse_begin_end_core(parser & p, pos_info const & pos, name const & end_token, bool nested = false) {
     if (!p.has_tactic_decls())
         throw parser_error("invalid 'begin-end' expression, tactic module has not been imported", pos);
-    environment env = open_tactic_namespace(p);
-    parser::local_scope scope2(p, env);
     parser::undef_id_to_local_scope scope1(p);
     p.next();
-    optional<expr> pre_tac = get_begin_end_pre_tactic(env);
+    optional<expr> pre_tac = get_begin_end_pre_tactic(p.env());
     buffer<expr> tacs;
     bool first = true;
 
@@ -223,7 +208,7 @@ static expr parse_begin_end_core(parser & p, pos_info const & pos, name const &
                 // parse: 'by' tactic
                 auto pos = p.pos();
                 p.next();
-                expr t = p.parse_expr();
+                expr t = p.parse_tactic();
                 add_tac(t, pos);
             } else {
                 throw parser_error("invalid 'have' tactic, 'by', 'begin', 'proof', or 'from' expected", p.pos());
@@ -237,7 +222,7 @@ static expr parse_begin_end_core(parser & p, pos_info const & pos, name const &
             add_tac(t, pos);
         } else {
             auto pos = p.pos();
-            expr t   = p.parse_expr();
+            expr t   = p.parse_tactic();
             add_tac(t, pos);
         }
     }
@@ -293,7 +278,7 @@ static expr parse_proof(parser & p, expr const & prop) {
         // parse: 'by' tactic
         auto pos = p.pos();
         p.next();
-        expr t = p.parse_expr();
+        expr t = p.parse_tactic();
         return p.mk_by(t, pos);
     } else if (p.curr_is_token(get_using_tk())) {
         // parse: 'using' locals* ',' proof
diff --git a/src/frontends/lean/parser.cpp b/src/frontends/lean/parser.cpp
index 5fc97870c..9281629e5 100644
--- a/src/frontends/lean/parser.cpp
+++ b/src/frontends/lean/parser.cpp
@@ -21,6 +21,7 @@ Author: Leonardo de Moura
 #include "kernel/error_msgs.h"
 #include "library/parser_nested_exception.h"
 #include "library/aliases.h"
+#include "library/constants.h"
 #include "library/private.h"
 #include "library/protected.h"
 #include "library/choice.h"
@@ -44,6 +45,7 @@ Author: Leonardo de Moura
 #include "frontends/lean/notation_cmd.h"
 #include "frontends/lean/elaborator.h"
 #include "frontends/lean/info_annotation.h"
+#include "frontends/lean/parse_rewrite_tactic.h"
 
 #ifndef LEAN_DEFAULT_PARSER_SHOW_ERRORS
 #define LEAN_DEFAULT_PARSER_SHOW_ERRORS true
@@ -1284,6 +1286,136 @@ expr parser::parse_scoped_expr(unsigned num_ps, expr const * ps, local_environme
     return parse_expr(rbp);
 }
 
+static bool is_tactic_type(expr const & e) {
+    return is_constant(e) && const_name(e) == get_tactic_name();
+}
+
+static bool is_tactic_expr_list_type(expr const & e) {
+    return is_constant(e) && const_name(e) == get_tactic_expr_list_name();
+}
+
+static bool is_tactic_opt_expr_list_type(expr const & e) {
+    return is_constant(e) && const_name(e) == get_tactic_opt_expr_list_name();
+}
+
+static bool is_tactic_command_type(expr e) {
+    while (is_pi(e))
+        e = binding_body(e);
+    return is_tactic_type(e);
+}
+
+optional<expr> parser::is_tactic_command(name & id) {
+    if (id.is_atomic())
+        id = get_tactic_name() + id;
+    auto d = m_env.find(id);
+    if (!d)
+        return none_expr();
+    expr type = d->get_type();
+    if (!is_tactic_command_type(type))
+        return none_expr();
+    return some_expr(type);
+}
+
+expr parser::parse_tactic_expr_list() {
+    auto p = pos();
+    check_token_next(get_lparen_tk(), "invalid tactic, '(' expected");
+    buffer<expr> args;
+    while (!curr_is_token(get_rparen_tk())) {
+        args.push_back(parse_expr());
+        if (!curr_is_token(get_comma_tk()))
+            break;
+        next();
+    }
+    check_token_next(get_rparen_tk(), "invalid tactic, ',' or ')' expected");
+    unsigned i = args.size();
+    expr r = save_pos(mk_constant(get_tactic_expr_list_nil_name()), p);
+    while (i > 0) {
+        i--;
+        r = mk_app({save_pos(mk_constant(get_tactic_expr_list_cons_name()), p), args[i], r}, p);
+    }
+    return r;
+}
+
+expr parser::parse_tactic_opt_expr_list() {
+    if (curr_is_token(get_lparen_tk())) {
+        return parse_tactic_expr_list();
+    } else if (curr_is_token(get_with_tk())) {
+        next();
+        return parse_tactic_expr_list();
+    } else {
+        return save_pos(mk_constant(get_tactic_expr_list_nil_name()), pos());
+    }
+}
+
+expr parser::parse_tactic_nud() {
+    if (curr_is_identifier()) {
+        auto id_pos = pos();
+        name id = get_name_val();
+        if (optional<expr> tac_type = is_tactic_command(id)) {
+            next();
+            expr type = *tac_type;
+            expr r = save_pos(mk_constant(id), id_pos);
+            while (is_pi(type)) {
+                expr d = binding_domain(type);
+                if (is_tactic_type(d)) {
+                    r = mk_app(r, parse_tactic(get_max_prec()), id_pos);
+                } else if (is_tactic_expr_list_type(d)) {
+                    r = mk_app(r, parse_tactic_expr_list(), id_pos);
+                } else if (is_tactic_opt_expr_list_type(d)) {
+                    r = mk_app(r, parse_tactic_opt_expr_list(), id_pos);
+                } else {
+                    r = mk_app(r, parse_expr(get_max_prec()), id_pos);
+                }
+                type = binding_body(type);
+            }
+            return r;
+        } else {
+            return parse_expr();
+        }
+    } else if (curr_is_token(get_lbracket_tk())) {
+        next();
+        expr r = parse_tactic();
+        while (curr_is_token(get_bar_tk())) {
+            auto bar_pos = pos();
+            next();
+            expr n = parse_tactic();
+            r = mk_app({save_pos(mk_constant(get_tactic_or_else_name()), bar_pos), r, n}, bar_pos);
+        }
+        check_token_next(get_rbracket_tk(), "invalid or-else tactic, ']' expected");
+        return r;
+    } else if (curr_is_token_or_id(get_rewrite_tk())) {
+        auto p = pos();
+        next();
+        return save_pos(parse_rewrite_tactic(*this), p);
+    } else if (curr_is_token(get_lparen_tk())) {
+        next();
+        expr r = parse_tactic();
+        check_token_next(get_rparen_tk(), "invalid tactic, ')' expected");
+        return r;
+    } else {
+        return parse_expr();
+    }
+}
+
+expr parser::parse_tactic_led(expr left) {
+    auto p = pos();
+    if (curr_is_token(get_semicolon_tk())) {
+        next();
+        expr right = parse_tactic();
+        return mk_app({save_pos(mk_constant(get_tactic_and_then_name()), p), left, right}, p);
+    } else {
+        throw parser_error("invalid tactic expression", p);
+    }
+}
+
+expr parser::parse_tactic(unsigned rbp) {
+    expr left = parse_tactic_nud();
+    while (rbp < curr_lbp()) {
+        left = parse_tactic_led(left);
+    }
+    return left;
+}
+
 void parser::parse_command() {
     lean_assert(curr() == scanner::token_kind::CommandKeyword);
     m_last_cmd_pos = pos();
diff --git a/src/frontends/lean/parser.h b/src/frontends/lean/parser.h
index 9f9a4a187..e861c0dc8 100644
--- a/src/frontends/lean/parser.h
+++ b/src/frontends/lean/parser.h
@@ -217,6 +217,12 @@ class parser {
     elaborator_context mk_elaborator_context(environment const & env, pos_info_provider const & pp);
     elaborator_context mk_elaborator_context(environment const & env, local_level_decls const & lls, pos_info_provider const & pp);
 
+    optional<expr> is_tactic_command(name & id);
+    expr parse_tactic_led(expr left);
+    expr parse_tactic_nud();
+    expr parse_tactic_expr_list();
+    expr parse_tactic_opt_expr_list();
+
 public:
     parser(environment const & env, io_state const & ios,
            std::istream & strm, char const * str_name,
@@ -380,6 +386,8 @@ public:
     }
     expr parse_scoped_expr(buffer<expr> const & ps, unsigned rbp = 0) { return parse_scoped_expr(ps.size(), ps.data(), rbp); }
 
+    expr parse_tactic(unsigned rbp = 0);
+
     struct local_scope { parser & m_p; environment m_env;
         local_scope(parser & p, bool save_options = false);
         local_scope(parser & p, environment const & env);
diff --git a/src/frontends/lean/token_table.cpp b/src/frontends/lean/token_table.cpp
index 26d7c01cc..2f474c839 100644
--- a/src/frontends/lean/token_table.cpp
+++ b/src/frontends/lean/token_table.cpp
@@ -79,7 +79,7 @@ void init_token_table(token_table & t) {
          {"from", 0}, {"(", g_max_prec}, {")", 0}, {"{", g_max_prec}, {"}", 0}, {"_", g_max_prec},
          {"[", g_max_prec}, {"]", 0}, {"⦃", g_max_prec}, {"⦄", 0}, {".{", 0}, {"Type", g_max_prec},
          {"{|", g_max_prec}, {"|}", 0}, {"⊢", 0}, {"⟨", g_max_prec}, {"⟩", 0}, {"^", 0}, {"↑", 0}, {"▸", 0},
-         {"using", 0}, {"|", 0}, {"!", g_max_prec}, {"?", 0},  {"with", 0}, {"...", 0}, {",", 0},
+         {"using", 0}, {"|", 0}, {"!", g_max_prec}, {"?", 0},  {"with", 0}, {"...", 0}, {",", 0}, {";", 1},
          {".", 0}, {":", 0}, {"::", 0}, {"calc", 0}, {"rewrite", 0}, {"esimp", 0}, {":=", 0}, {"--", 0}, {"#", 0},
          {"(*", 0}, {"/-", 0}, {"begin", g_max_prec}, {"proof", g_max_prec}, {"qed", 0}, {"@", g_max_prec},
          {"sorry", g_max_prec}, {"+", g_plus_prec}, {g_cup, g_cup_prec}, {"->", g_arrow_prec},
diff --git a/src/frontends/lean/tokens.cpp b/src/frontends/lean/tokens.cpp
index e360b8550..1b691239f 100644
--- a/src/frontends/lean/tokens.cpp
+++ b/src/frontends/lean/tokens.cpp
@@ -10,6 +10,7 @@ namespace lean {
 static name * g_period       = nullptr;
 static name * g_placeholder  = nullptr;
 static name * g_colon        = nullptr;
+static name * g_semicolon    = nullptr;
 static name * g_dcolon       = nullptr;
 static name * g_lparen       = nullptr;
 static name * g_rparen       = nullptr;
@@ -81,6 +82,7 @@ static name * g_using        = nullptr;
 static name * g_then         = nullptr;
 static name * g_else         = nullptr;
 static name * g_by           = nullptr;
+static name * g_rewrite      = nullptr;
 static name * g_proof        = nullptr;
 static name * g_qed          = nullptr;
 static name * g_begin        = nullptr;
@@ -130,6 +132,7 @@ void initialize_tokens() {
     g_period       = new name(".");
     g_placeholder  = new name("_");
     g_colon        = new name(":");
+    g_semicolon    = new name(";");
     g_dcolon       = new name("::");
     g_lparen       = new name("(");
     g_rparen       = new name(")");
@@ -201,6 +204,7 @@ void initialize_tokens() {
     g_then         = new name("then");
     g_else         = new name("else");
     g_by           = new name("by");
+    g_rewrite      = new name("rewrite");
     g_proof        = new name("proof");
     g_qed          = new name("qed");
     g_begin        = new name("begin");
@@ -297,6 +301,7 @@ void finalize_tokens() {
     delete g_then;
     delete g_else;
     delete g_by;
+    delete g_rewrite;
     delete g_proof;
     delete g_qed;
     delete g_begin;
@@ -363,6 +368,7 @@ void finalize_tokens() {
     delete g_rparen;
     delete g_lparen;
     delete g_colon;
+    delete g_semicolon;
     delete g_dcolon;
     delete g_placeholder;
     delete g_period;
@@ -372,6 +378,7 @@ name const & get_metaclasses_tk() { return *g_metaclasses; }
 name const & get_period_tk() { return *g_period; }
 name const & get_placeholder_tk() { return *g_placeholder; }
 name const & get_colon_tk() { return *g_colon; }
+name const & get_semicolon_tk() { return *g_semicolon; }
 name const & get_dcolon_tk() { return *g_dcolon; }
 name const & get_langle_tk() { return *g_langle; }
 name const & get_rangle_tk() { return *g_rangle; }
@@ -443,6 +450,7 @@ name const & get_using_tk() { return *g_using; }
 name const & get_then_tk() { return *g_then; }
 name const & get_else_tk() { return *g_else; }
 name const & get_by_tk() { return *g_by; }
+name const & get_rewrite_tk() { return *g_rewrite; }
 name const & get_proof_tk() { return *g_proof; }
 name const & get_qed_tk() { return *g_qed; }
 name const & get_begin_tk() { return *g_begin; }
diff --git a/src/frontends/lean/tokens.h b/src/frontends/lean/tokens.h
index 3005615d8..4fffd620f 100644
--- a/src/frontends/lean/tokens.h
+++ b/src/frontends/lean/tokens.h
@@ -12,6 +12,7 @@ void finalize_tokens();
 name const & get_period_tk();
 name const & get_placeholder_tk();
 name const & get_colon_tk();
+name const & get_semicolon_tk();
 name const & get_dcolon_tk();
 name const & get_lparen_tk();
 name const & get_rparen_tk();
@@ -83,6 +84,7 @@ name const & get_using_tk();
 name const & get_then_tk();
 name const & get_else_tk();
 name const & get_by_tk();
+name const & get_rewrite_tk();
 name const & get_proof_tk();
 name const & get_begin_tk();
 name const & get_qed_tk();
diff --git a/src/library/constants.cpp b/src/library/constants.cpp
index 2c413a2c4..d1e4395ca 100644
--- a/src/library/constants.cpp
+++ b/src/library/constants.cpp
@@ -69,16 +69,14 @@ name const * g_tactic_assumption = nullptr;
 name const * g_tactic_at_most = nullptr;
 name const * g_tactic_beta = nullptr;
 name const * g_tactic_builtin = nullptr;
-name const * g_tactic_change_goal = nullptr;
-name const * g_tactic_change_hypothesis = nullptr;
+name const * g_tactic_cases = nullptr;
+name const * g_tactic_change = nullptr;
 name const * g_tactic_clear = nullptr;
-name const * g_tactic_clear_lst = nullptr;
+name const * g_tactic_clears = nullptr;
 name const * g_tactic_determ = nullptr;
 name const * g_tactic_discard = nullptr;
 name const * g_tactic_intro = nullptr;
-name const * g_tactic_intro_lst = nullptr;
-name const * g_tactic_inversion = nullptr;
-name const * g_tactic_inversion_with = nullptr;
+name const * g_tactic_intros = nullptr;
 name const * g_tactic_exact = nullptr;
 name const * g_tactic_expr = nullptr;
 name const * g_tactic_expr_builtin = nullptr;
@@ -89,17 +87,18 @@ name const * g_tactic_fail = nullptr;
 name const * g_tactic_fixpoint = nullptr;
 name const * g_tactic_focus_at = nullptr;
 name const * g_tactic_generalize = nullptr;
-name const * g_tactic_generalize_lst = nullptr;
+name const * g_tactic_generalizes = nullptr;
 name const * g_tactic_id = nullptr;
 name const * g_tactic_interleave = nullptr;
 name const * g_tactic_now = nullptr;
+name const * g_tactic_opt_expr_list = nullptr;
 name const * g_tactic_or_else = nullptr;
 name const * g_tactic_par = nullptr;
 name const * g_tactic_state = nullptr;
 name const * g_tactic_rename = nullptr;
 name const * g_tactic_repeat = nullptr;
 name const * g_tactic_revert = nullptr;
-name const * g_tactic_revert_lst = nullptr;
+name const * g_tactic_reverts = nullptr;
 name const * g_tactic_rotate_left = nullptr;
 name const * g_tactic_rotate_right = nullptr;
 name const * g_tactic_trace = nullptr;
@@ -180,16 +179,14 @@ void initialize_constants() {
     g_tactic_at_most = new name{"tactic", "at_most"};
     g_tactic_beta = new name{"tactic", "beta"};
     g_tactic_builtin = new name{"tactic", "builtin"};
-    g_tactic_change_goal = new name{"tactic", "change_goal"};
-    g_tactic_change_hypothesis = new name{"tactic", "change_hypothesis"};
+    g_tactic_cases = new name{"tactic", "cases"};
+    g_tactic_change = new name{"tactic", "change"};
     g_tactic_clear = new name{"tactic", "clear"};
-    g_tactic_clear_lst = new name{"tactic", "clear_lst"};
+    g_tactic_clears = new name{"tactic", "clears"};
     g_tactic_determ = new name{"tactic", "determ"};
     g_tactic_discard = new name{"tactic", "discard"};
     g_tactic_intro = new name{"tactic", "intro"};
-    g_tactic_intro_lst = new name{"tactic", "intro_lst"};
-    g_tactic_inversion = new name{"tactic", "inversion"};
-    g_tactic_inversion_with = new name{"tactic", "inversion_with"};
+    g_tactic_intros = new name{"tactic", "intros"};
     g_tactic_exact = new name{"tactic", "exact"};
     g_tactic_expr = new name{"tactic", "expr"};
     g_tactic_expr_builtin = new name{"tactic", "expr", "builtin"};
@@ -200,17 +197,18 @@ void initialize_constants() {
     g_tactic_fixpoint = new name{"tactic", "fixpoint"};
     g_tactic_focus_at = new name{"tactic", "focus_at"};
     g_tactic_generalize = new name{"tactic", "generalize"};
-    g_tactic_generalize_lst = new name{"tactic", "generalize_lst"};
+    g_tactic_generalizes = new name{"tactic", "generalizes"};
     g_tactic_id = new name{"tactic", "id"};
     g_tactic_interleave = new name{"tactic", "interleave"};
     g_tactic_now = new name{"tactic", "now"};
+    g_tactic_opt_expr_list = new name{"tactic", "opt_expr_list"};
     g_tactic_or_else = new name{"tactic", "or_else"};
     g_tactic_par = new name{"tactic", "par"};
     g_tactic_state = new name{"tactic", "state"};
     g_tactic_rename = new name{"tactic", "rename"};
     g_tactic_repeat = new name{"tactic", "repeat"};
     g_tactic_revert = new name{"tactic", "revert"};
-    g_tactic_revert_lst = new name{"tactic", "revert_lst"};
+    g_tactic_reverts = new name{"tactic", "reverts"};
     g_tactic_rotate_left = new name{"tactic", "rotate_left"};
     g_tactic_rotate_right = new name{"tactic", "rotate_right"};
     g_tactic_trace = new name{"tactic", "trace"};
@@ -292,16 +290,14 @@ void finalize_constants() {
     delete g_tactic_at_most;
     delete g_tactic_beta;
     delete g_tactic_builtin;
-    delete g_tactic_change_goal;
-    delete g_tactic_change_hypothesis;
+    delete g_tactic_cases;
+    delete g_tactic_change;
     delete g_tactic_clear;
-    delete g_tactic_clear_lst;
+    delete g_tactic_clears;
     delete g_tactic_determ;
     delete g_tactic_discard;
     delete g_tactic_intro;
-    delete g_tactic_intro_lst;
-    delete g_tactic_inversion;
-    delete g_tactic_inversion_with;
+    delete g_tactic_intros;
     delete g_tactic_exact;
     delete g_tactic_expr;
     delete g_tactic_expr_builtin;
@@ -312,17 +308,18 @@ void finalize_constants() {
     delete g_tactic_fixpoint;
     delete g_tactic_focus_at;
     delete g_tactic_generalize;
-    delete g_tactic_generalize_lst;
+    delete g_tactic_generalizes;
     delete g_tactic_id;
     delete g_tactic_interleave;
     delete g_tactic_now;
+    delete g_tactic_opt_expr_list;
     delete g_tactic_or_else;
     delete g_tactic_par;
     delete g_tactic_state;
     delete g_tactic_rename;
     delete g_tactic_repeat;
     delete g_tactic_revert;
-    delete g_tactic_revert_lst;
+    delete g_tactic_reverts;
     delete g_tactic_rotate_left;
     delete g_tactic_rotate_right;
     delete g_tactic_trace;
@@ -403,16 +400,14 @@ name const & get_tactic_assumption_name() { return *g_tactic_assumption; }
 name const & get_tactic_at_most_name() { return *g_tactic_at_most; }
 name const & get_tactic_beta_name() { return *g_tactic_beta; }
 name const & get_tactic_builtin_name() { return *g_tactic_builtin; }
-name const & get_tactic_change_goal_name() { return *g_tactic_change_goal; }
-name const & get_tactic_change_hypothesis_name() { return *g_tactic_change_hypothesis; }
+name const & get_tactic_cases_name() { return *g_tactic_cases; }
+name const & get_tactic_change_name() { return *g_tactic_change; }
 name const & get_tactic_clear_name() { return *g_tactic_clear; }
-name const & get_tactic_clear_lst_name() { return *g_tactic_clear_lst; }
+name const & get_tactic_clears_name() { return *g_tactic_clears; }
 name const & get_tactic_determ_name() { return *g_tactic_determ; }
 name const & get_tactic_discard_name() { return *g_tactic_discard; }
 name const & get_tactic_intro_name() { return *g_tactic_intro; }
-name const & get_tactic_intro_lst_name() { return *g_tactic_intro_lst; }
-name const & get_tactic_inversion_name() { return *g_tactic_inversion; }
-name const & get_tactic_inversion_with_name() { return *g_tactic_inversion_with; }
+name const & get_tactic_intros_name() { return *g_tactic_intros; }
 name const & get_tactic_exact_name() { return *g_tactic_exact; }
 name const & get_tactic_expr_name() { return *g_tactic_expr; }
 name const & get_tactic_expr_builtin_name() { return *g_tactic_expr_builtin; }
@@ -423,17 +418,18 @@ name const & get_tactic_fail_name() { return *g_tactic_fail; }
 name const & get_tactic_fixpoint_name() { return *g_tactic_fixpoint; }
 name const & get_tactic_focus_at_name() { return *g_tactic_focus_at; }
 name const & get_tactic_generalize_name() { return *g_tactic_generalize; }
-name const & get_tactic_generalize_lst_name() { return *g_tactic_generalize_lst; }
+name const & get_tactic_generalizes_name() { return *g_tactic_generalizes; }
 name const & get_tactic_id_name() { return *g_tactic_id; }
 name const & get_tactic_interleave_name() { return *g_tactic_interleave; }
 name const & get_tactic_now_name() { return *g_tactic_now; }
+name const & get_tactic_opt_expr_list_name() { return *g_tactic_opt_expr_list; }
 name const & get_tactic_or_else_name() { return *g_tactic_or_else; }
 name const & get_tactic_par_name() { return *g_tactic_par; }
 name const & get_tactic_state_name() { return *g_tactic_state; }
 name const & get_tactic_rename_name() { return *g_tactic_rename; }
 name const & get_tactic_repeat_name() { return *g_tactic_repeat; }
 name const & get_tactic_revert_name() { return *g_tactic_revert; }
-name const & get_tactic_revert_lst_name() { return *g_tactic_revert_lst; }
+name const & get_tactic_reverts_name() { return *g_tactic_reverts; }
 name const & get_tactic_rotate_left_name() { return *g_tactic_rotate_left; }
 name const & get_tactic_rotate_right_name() { return *g_tactic_rotate_right; }
 name const & get_tactic_trace_name() { return *g_tactic_trace; }
diff --git a/src/library/constants.h b/src/library/constants.h
index b1a6df776..6ec469c09 100644
--- a/src/library/constants.h
+++ b/src/library/constants.h
@@ -71,16 +71,14 @@ name const & get_tactic_assumption_name();
 name const & get_tactic_at_most_name();
 name const & get_tactic_beta_name();
 name const & get_tactic_builtin_name();
-name const & get_tactic_change_goal_name();
-name const & get_tactic_change_hypothesis_name();
+name const & get_tactic_cases_name();
+name const & get_tactic_change_name();
 name const & get_tactic_clear_name();
-name const & get_tactic_clear_lst_name();
+name const & get_tactic_clears_name();
 name const & get_tactic_determ_name();
 name const & get_tactic_discard_name();
 name const & get_tactic_intro_name();
-name const & get_tactic_intro_lst_name();
-name const & get_tactic_inversion_name();
-name const & get_tactic_inversion_with_name();
+name const & get_tactic_intros_name();
 name const & get_tactic_exact_name();
 name const & get_tactic_expr_name();
 name const & get_tactic_expr_builtin_name();
@@ -91,17 +89,18 @@ name const & get_tactic_fail_name();
 name const & get_tactic_fixpoint_name();
 name const & get_tactic_focus_at_name();
 name const & get_tactic_generalize_name();
-name const & get_tactic_generalize_lst_name();
+name const & get_tactic_generalizes_name();
 name const & get_tactic_id_name();
 name const & get_tactic_interleave_name();
 name const & get_tactic_now_name();
+name const & get_tactic_opt_expr_list_name();
 name const & get_tactic_or_else_name();
 name const & get_tactic_par_name();
 name const & get_tactic_state_name();
 name const & get_tactic_rename_name();
 name const & get_tactic_repeat_name();
 name const & get_tactic_revert_name();
-name const & get_tactic_revert_lst_name();
+name const & get_tactic_reverts_name();
 name const & get_tactic_rotate_left_name();
 name const & get_tactic_rotate_right_name();
 name const & get_tactic_trace_name();
diff --git a/src/library/constants.txt b/src/library/constants.txt
index c443389e4..348406140 100644
--- a/src/library/constants.txt
+++ b/src/library/constants.txt
@@ -64,16 +64,14 @@ tactic.assumption
 tactic.at_most
 tactic.beta
 tactic.builtin
-tactic.change_goal
-tactic.change_hypothesis
+tactic.cases
+tactic.change
 tactic.clear
-tactic.clear_lst
+tactic.clears
 tactic.determ
 tactic.discard
 tactic.intro
-tactic.intro_lst
-tactic.inversion
-tactic.inversion_with
+tactic.intros
 tactic.exact
 tactic.expr
 tactic.expr.builtin
@@ -84,17 +82,18 @@ tactic.fail
 tactic.fixpoint
 tactic.focus_at
 tactic.generalize
-tactic.generalize_lst
+tactic.generalizes
 tactic.id
 tactic.interleave
 tactic.now
+tactic.opt_expr_list
 tactic.or_else
 tactic.par
 tactic.state
 tactic.rename
 tactic.repeat
 tactic.revert
-tactic.revert_lst
+tactic.reverts
 tactic.rotate_left
 tactic.rotate_right
 tactic.trace
diff --git a/src/library/tactic/change_tactic.cpp b/src/library/tactic/change_tactic.cpp
index e0d1158f6..1a463cfd3 100644
--- a/src/library/tactic/change_tactic.cpp
+++ b/src/library/tactic/change_tactic.cpp
@@ -45,7 +45,7 @@ tactic change_goal_tactic(elaborate_fn const & elab, expr const & e) {
 }
 
 void initialize_change_tactic() {
-    register_tac(get_tactic_change_goal_name(),
+    register_tac(get_tactic_change_name(),
                  [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
                      check_tactic_expr(app_arg(e), "invalid 'change' tactic, invalid argument");
                      return change_goal_tactic(fn, get_tactic_expr_expr(app_arg(e)));
diff --git a/src/library/tactic/clear_tactic.cpp b/src/library/tactic/clear_tactic.cpp
index ff37c0528..d0288a57c 100644
--- a/src/library/tactic/clear_tactic.cpp
+++ b/src/library/tactic/clear_tactic.cpp
@@ -48,7 +48,7 @@ void initialize_clear_tactic() {
                      name n = tactic_expr_to_id(app_arg(e), "invalid 'clear' tactic, argument must be an identifier");
                      return clear_tactic(n);
                  });
-    register_tac(get_tactic_clear_lst_name(),
+    register_tac(get_tactic_clears_name(),
                  [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
                      buffer<name> ns;
                      get_tactic_id_list_elements(app_arg(e), ns, "invalid 'clears' tactic, list of identifiers expected");
diff --git a/src/library/tactic/generalize_tactic.cpp b/src/library/tactic/generalize_tactic.cpp
index cf6414ec6..3dd13f5f1 100644
--- a/src/library/tactic/generalize_tactic.cpp
+++ b/src/library/tactic/generalize_tactic.cpp
@@ -68,7 +68,7 @@ void initialize_generalize_tactic() {
                      return generalize_tactic(fn, get_tactic_expr_expr(app_arg(e)), "x");
                  });
 
-    register_tac(get_tactic_generalize_lst_name(),
+    register_tac(get_tactic_generalizes_name(),
                  [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
                      buffer<expr> args;
                      get_tactic_expr_list_elements(app_arg(e), args, "invalid 'generalizes' tactic, list of expressions expected");
diff --git a/src/library/tactic/intros_tactic.cpp b/src/library/tactic/intros_tactic.cpp
index d5bf3ba45..c62519179 100644
--- a/src/library/tactic/intros_tactic.cpp
+++ b/src/library/tactic/intros_tactic.cpp
@@ -65,7 +65,7 @@ void initialize_intros_tactic() {
                      name const & id = tactic_expr_to_id(app_arg(e), "invalid 'intro' tactic, argument must be an identifier");
                      return intros_tactic(to_list(id));
                  });
-    register_tac(get_tactic_intro_lst_name(),
+    register_tac(get_tactic_intros_name(),
                  [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
                      buffer<name> ns;
                      get_tactic_id_list_elements(app_arg(e), ns, "invalid 'intros' tactic, arguments must be identifiers");
diff --git a/src/library/tactic/inversion_tactic.cpp b/src/library/tactic/inversion_tactic.cpp
index a82715468..3067c2503 100644
--- a/src/library/tactic/inversion_tactic.cpp
+++ b/src/library/tactic/inversion_tactic.cpp
@@ -962,16 +962,11 @@ tactic inversion_tactic(name const & n, list<name> const & ids) {
 }
 
 void initialize_inversion_tactic() {
-    register_tac(get_tactic_inversion_name(),
+    register_tac(get_tactic_cases_name(),
                  [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
-                     name n = tactic_expr_to_id(app_arg(e), "invalid 'inversion/cases' tactic, argument must be an identifier");
-                     return inversion_tactic(n, list<name>());
-                 });
-    register_tac(get_tactic_inversion_with_name(),
-                 [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
-                     name n = tactic_expr_to_id(app_arg(app_fn(e)), "invalid 'cases-with' tactic, argument must be an identifier");
+                     name n = tactic_expr_to_id(app_arg(app_fn(e)), "invalid 'cases' tactic, argument must be an identifier");
                      buffer<name> ids;
-                     get_tactic_id_list_elements(app_arg(e), ids, "invalid 'cases-with' tactic, list of identifiers expected");
+                     get_tactic_id_list_elements(app_arg(e), ids, "invalid 'cases' tactic, list of identifiers expected");
                      return inversion_tactic(n, to_list(ids.begin(), ids.end()));
                  });
 }
diff --git a/src/library/tactic/revert_tactic.cpp b/src/library/tactic/revert_tactic.cpp
index 365d70295..6d22a7acb 100644
--- a/src/library/tactic/revert_tactic.cpp
+++ b/src/library/tactic/revert_tactic.cpp
@@ -55,7 +55,7 @@ void initialize_revert_tactic() {
                      return revert_tactic(n);
                  });
 
-    register_tac(get_tactic_revert_lst_name(),
+    register_tac(get_tactic_reverts_name(),
                  [](type_checker &, elaborate_fn const &, expr const & e, pos_info_provider const *) {
                      buffer<name> ns;
                      get_tactic_id_list_elements(app_arg(e), ns, "invalid 'reverts' tactic, list of identifiers expected");
diff --git a/tests/lean/change_tac_fail.lean b/tests/lean/change_tac_fail.lean
index 1718ee7e3..062132a9b 100644
--- a/tests/lean/change_tac_fail.lean
+++ b/tests/lean/change_tac_fail.lean
@@ -7,6 +7,6 @@ theorem append.assoc : ∀ (s t u : list T), s ++ t ++ u = s ++ (t ++ u)
 | append.assoc nil t u      := by esimp
 | append.assoc (a :: l) t u :=
   begin
-    change a :: (l ++ t ++ u) = (a :: l) ++ (t ++ a),
+    change (a :: (l ++ t ++ u) = (a :: l) ++ (t ++ a)),
     rewrite append.assoc
   end
diff --git a/tests/lean/change_tac_fail.lean.expected.out b/tests/lean/change_tac_fail.lean.expected.out
index 4778a96b7..94ca3d0f7 100644
--- a/tests/lean/change_tac_fail.lean.expected.out
+++ b/tests/lean/change_tac_fail.lean.expected.out
@@ -1,4 +1,4 @@
-change_tac_fail.lean:10:47: error: type mismatch at application
+change_tac_fail.lean:10:48: error: type mismatch at application
   t ++ a
 term
   a
diff --git a/tests/lean/empty_thm.lean b/tests/lean/empty_thm.lean
index 47c975a06..1af981a5c 100644
--- a/tests/lean/empty_thm.lean
+++ b/tests/lean/empty_thm.lean
@@ -1,7 +1,7 @@
 import logic
 open tactic
 
-definition simple := apply trivial
+definition simple := apply _root_.trivial
 
 tactic_hint simple
 
diff --git a/tests/lean/run/def_tac.lean b/tests/lean/run/def_tac.lean
index d160262ea..2f4f7ec82 100644
--- a/tests/lean/run/def_tac.lean
+++ b/tests/lean/run/def_tac.lean
@@ -1,15 +1,15 @@
 context
   open tactic
   definition cases_refl (e : expr) : tactic :=
-  cases e; apply rfl
+  cases e expr_list.nil; apply rfl
 
   definition cases_lst_refl : expr_list → tactic
   | cases_lst_refl expr_list.nil        := apply rfl
-  | cases_lst_refl (expr_list.cons a l) := cases a; cases_lst_refl l
+  | cases_lst_refl (expr_list.cons a l) := cases a expr_list.nil; cases_lst_refl l
 
   -- Similar to cases_refl, but make sure the argument is not an arbitrary expression.
   definition eq_rec {A : Type} {a b : A} (e : a = b) : tactic :=
-  cases e; apply rfl
+  cases e expr_list.nil; apply rfl
 end
 
 notation `cases_lst` l:(foldr `,` (h t, tactic.expr_list.cons h t) tactic.expr_list.nil) := cases_lst_refl l
diff --git a/tests/lean/run/inf_tree3.lean b/tests/lean/run/inf_tree3.lean
index c6eebb6e1..9daf53db4 100644
--- a/tests/lean/run/inf_tree3.lean
+++ b/tests/lean/run/inf_tree3.lean
@@ -14,7 +14,7 @@ namespace inftree
                                       (t : inftree A) (ht : acc dsub t) : acc dsub (node f t) :=
   acc.intro (node f t) (λ (y : inftree A) (hlt : dsub y (node f t)),
     begin
-      inversion hlt,
+      cases hlt,
       apply (hf a),
       apply ht
     end)
diff --git a/tests/lean/run/rename_tac.lean b/tests/lean/run/rename_tac.lean
index 1c27b8cd0..13bd2d991 100644
--- a/tests/lean/run/rename_tac.lean
+++ b/tests/lean/run/rename_tac.lean
@@ -12,7 +12,7 @@ end
 theorem foo2 (A : Type) (a b c : A) (Hab : a = b) (Hbc : b = c) : a = c :=
 begin
   apply eq.trans,
-  Hab ↦ Foo,
+  rename Hab Foo,
   apply Foo,
   apply Hbc,
 end
diff --git a/tests/lean/run/tactic_op_overload_bug.lean b/tests/lean/run/tactic_op_overload_bug.lean
new file mode 100644
index 000000000..2a2e15307
--- /dev/null
+++ b/tests/lean/run/tactic_op_overload_bug.lean
@@ -0,0 +1,27 @@
+import data.num data.bool
+
+open bool well_founded
+
+namespace pos_num
+
+definition lt_pred (a b : pos_num) : Prop := lt a b = tt
+
+definition not_lt_one1 (a : pos_num) : ¬ lt_pred a one :=
+begin
+  esimp {lt_pred},
+  intro H,
+  apply (absurd_of_eq_ff_of_eq_tt (lt_one_right_eq_ff a) H)
+end
+
+open tactic well_founded
+
+print raw intro -- intro is overloaded
+
+definition not_lt_one2 (a : pos_num) : ¬ lt_pred a one :=
+begin
+  esimp {lt_pred},
+  intro H,
+  apply (absurd_of_eq_ff_of_eq_tt (lt_one_right_eq_ff a) H)
+end
+
+end pos_num