diff --git a/library/init/meta/tactic.lean b/library/init/meta/tactic.lean
index e2f09256e9..7be0787847 100644
--- a/library/init/meta/tactic.lean
+++ b/library/init/meta/tactic.lean
@@ -223,7 +223,12 @@ meta constant rename        : name → name → tactic unit
 meta constant clear         : expr → tactic unit
 meta constant revert_lst    : list expr → tactic nat
 meta constant whnf_core     : transparency → expr → tactic expr
+/- eta expand the given expression -/
 meta constant eta_expand    : expr → tactic expr
+/- beta reduction -/
+meta constant beta          : expr → tactic expr
+/- zeta reduction -/
+meta constant zeta          : expr → tactic expr
 meta constant unify_core    : transparency → expr → expr → tactic unit
 /- is_def_eq_core is similar to unify_core, but it treats metavariables as constants. -/
 meta constant is_def_eq_core : transparency → expr → expr → tactic unit
diff --git a/src/library/tactic/tactic_state.cpp b/src/library/tactic/tactic_state.cpp
index a8c20440dd..f87a515607 100644
--- a/src/library/tactic/tactic_state.cpp
+++ b/src/library/tactic/tactic_state.cpp
@@ -7,6 +7,7 @@ Author: Leonardo de Moura
 #include "util/fresh_name.h"
 #include "util/sexpr/option_declarations.h"
 #include "kernel/type_checker.h"
+#include "kernel/instantiate.h"
 #include "library/constants.h"
 #include "library/type_context.h"
 #include "library/pp_options.h"
@@ -381,6 +382,27 @@ vm_obj tactic_eta_expand(vm_obj const & e, vm_obj const & s0) {
     }
 }
 
+vm_obj tactic_beta(vm_obj const & e, vm_obj const & s0) {
+    tactic_state const & s = to_tactic_state(s0);
+    try {
+        return mk_tactic_success(to_obj(head_beta_reduce(to_expr(e))), s);
+    } catch (exception & ex) {
+        return mk_tactic_exception(ex, s);
+    }
+}
+
+vm_obj tactic_zeta(vm_obj const & e0, vm_obj const & s0) {
+    expr const & e = to_expr(e0);
+    tactic_state const & s = to_tactic_state(s0);
+    if (!is_local(e)) return mk_tactic_success(e0, s);
+    optional<metavar_decl> mdecl = s.get_main_goal_decl();
+    if (!mdecl) return mk_tactic_success(e0, s);
+    local_context lctx = mdecl->get_context();
+    optional<local_decl> ldecl = lctx.get_local_decl(e);
+    if (!ldecl || !ldecl->get_value()) return mk_tactic_success(e0, s);
+    return mk_tactic_success(to_obj(*ldecl->get_value()), s);
+}
+
 vm_obj tactic_is_class(vm_obj const & e, vm_obj const & s0) {
     tactic_state const & s = to_tactic_state(s0);
     type_context ctx       = mk_type_context_for(s);
@@ -600,6 +622,8 @@ void initialize_tactic_state() {
     DECLARE_VM_BUILTIN(name({"tactic", "whnf_core"}),            tactic_whnf_core);
     DECLARE_VM_BUILTIN(name({"tactic", "is_def_eq_core"}),       tactic_is_def_eq_core);
     DECLARE_VM_BUILTIN(name({"tactic", "eta_expand"}),           tactic_eta_expand);
+    DECLARE_VM_BUILTIN(name({"tactic", "beta"}),                 tactic_beta);
+    DECLARE_VM_BUILTIN(name({"tactic", "zeta"}),                 tactic_zeta);
     DECLARE_VM_BUILTIN(name({"tactic", "is_class"}),             tactic_is_class);
     DECLARE_VM_BUILTIN(name({"tactic", "mk_instance"}),          tactic_mk_instance);
     DECLARE_VM_BUILTIN(name({"tactic", "unify_core"}),           tactic_unify_core);
diff --git a/tests/lean/run/beta_zeta.lean b/tests/lean/run/beta_zeta.lean
new file mode 100644
index 0000000000..6de2a8e7dd
--- /dev/null
+++ b/tests/lean/run/beta_zeta.lean
@@ -0,0 +1,20 @@
+open tactic
+
+meta def check_expr (p : pexpr) (t : expr) : tactic unit :=
+do e ← to_expr p, guard (t = e)
+
+example : true :=
+let x := 10 in
+by do h ← get_local `x,
+      zeta h >>= check_expr `(10),
+      triv
+
+example : let x := 10 in true :=
+by do x ← intro1,
+      zeta x >>= check_expr `(10),
+      triv
+
+example : true :=
+by do h ← to_expr `((λ x : nat, x + 1) 1),
+      beta h >>= check_expr `(1 + 1),
+      triv