diff --git a/src/tests/library/CMakeLists.txt b/src/tests/library/CMakeLists.txt
index fa8376974..2c99c3253 100644
--- a/src/tests/library/CMakeLists.txt
+++ b/src/tests/library/CMakeLists.txt
@@ -1,3 +1,6 @@
+add_executable(implicit_args implicit_args.cpp)
+target_link_libraries(implicit_args ${EXTRA_LIBS})
+add_test(implicit_args ${CMAKE_CURRENT_BINARY_DIR}/implicit_args)
 add_executable(beta beta.cpp)
 target_link_libraries(beta ${EXTRA_LIBS})
 add_test(beta ${CMAKE_CURRENT_BINARY_DIR}/beta)
diff --git a/src/tests/library/implicit_args.cpp b/src/tests/library/implicit_args.cpp
new file mode 100644
index 000000000..16d639aa5
--- /dev/null
+++ b/src/tests/library/implicit_args.cpp
@@ -0,0 +1,463 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "test.h"
+#include "metavar_env.h"
+#include "elaborator.h"
+#include "printer.h"
+#include "occurs.h"
+#include "abstract.h"
+#include "toplevel.h"
+#include "basic_thms.h"
+#include "kernel_exception.h"
+using namespace lean;
+
+static name g_placeholder_name(name(name(name(0u), "library"), "placeholder"));
+/** \brief Return a new placeholder expression. To be able to track location,
+    a new constant for each placeholder.
+*/
+expr mk_placholder() {
+    return mk_constant(g_placeholder_name);
+}
+
+/** \brief Return true iff the given expression is a placeholder. */
+bool is_placeholder(expr const & e) {
+    return is_constant(e) && const_name(e) == g_placeholder_name;
+}
+
+/** \brief Return true iff the given expression contains placeholders. */
+bool has_placeholder(expr const & e) {
+    return occurs(mk_placholder(), e);
+}
+
+std::ostream & operator<<(std::ostream & out, metavar_env const & uf) { uf.display(out); return out; }
+
+/**
+   \brief Auxiliary function for #replace_placeholders_with_metavars
+*/
+static expr replace(expr const & e, context const & ctx, metavar_env & menv) {
+    switch (e.kind()) {
+    case expr_kind::Constant:
+        if (is_placeholder(e)) {
+            return menv.mk_metavar(ctx);
+        } else {
+            return e;
+        }
+    case expr_kind::Var: case expr_kind::Type: case expr_kind::Value:
+        return e;
+    case expr_kind::App:
+        return update_app(e, [&](expr const & c) { return replace(c, ctx, menv); });
+    case expr_kind::Eq:
+        return update_eq(e, [&](expr const & l, expr const & r) { return mk_pair(replace(l, ctx, menv), replace(r, ctx, menv)); });
+    case expr_kind::Lambda:
+    case expr_kind::Pi:
+        return update_abst(e, [&](expr const & d, expr const & b) {
+                expr new_d = replace(d, ctx, menv);
+                expr new_b = replace(b, extend(ctx, abst_name(e), new_d), menv);
+                return mk_pair(new_d, new_b);
+            });
+    case expr_kind::Let:
+        return update_let(e, [&](expr const & v, expr const & b) {
+                expr new_v = replace(v, ctx, menv);
+                expr new_b = replace(b, extend(ctx, abst_name(e), expr(), new_v), menv);
+                return mk_pair(new_v, new_b);
+            });
+    }
+    lean_unreachable();
+    return e;
+}
+
+/**
+   \brief Replace placeholders with fresh meta-variables.
+*/
+expr replace_placeholders_with_metavars(expr const & e, metavar_env & menv) {
+    return replace(e, context(), menv);
+}
+
+expr elaborate(elaborator & elb, expr const & e) {
+    expr new_e = replace_placeholders_with_metavars(e, elb.menv());
+    return elb(new_e);
+}
+
+static void tst1() {
+    expr m1 = mk_metavar(0);
+    expr m2 = mk_metavar(1);
+    expr a  = Const("a");
+    expr f  = Const("f");
+    lean_assert(is_metavar(m1));
+    lean_assert(!is_metavar(a));
+    lean_assert(metavar_idx(m1) == 0);
+    lean_assert(metavar_idx(m2) == 1);
+    lean_assert(m1 != m2);
+    lean_assert(a != m1);
+    std::cout << m1 << " " << m2 << "\n";
+    lean_assert(has_metavar(m1));
+    lean_assert(has_metavar(f(f(f(m1)))));
+    lean_assert(!has_metavar(f(f(a))));
+}
+
+static void tst2() {
+    environment env;
+    metavar_env u(env);
+    expr m1 = u.mk_metavar();
+    expr m2 = u.mk_metavar();
+    expr m3 = u.mk_metavar();
+    lean_assert(!u.is_assigned(m1));
+    lean_assert(!u.is_assigned(m2));
+    lean_assert(!u.is_assigned(m3));
+    expr f = Const("f");
+    expr t1 = f(m1, m2);
+    expr t2 = f(m1, m1);
+    lean_assert(t1 != t2);
+    lean_assert(!u.is_modulo_eq(t1, t2));
+    // m1 <- m2
+    u.assign(m1, m2);
+    std::cout << u << "\n";
+    lean_assert(u.root(m2) == m2);
+    lean_assert(u.root(m1) == m2);
+    lean_assert(u.is_modulo_eq(t1, t2));
+    expr a = Const("a");
+    expr b = Const("b");
+    expr g = Const("g");
+    expr t3 = f(a, m1);
+    expr t4 = f(m2, a);
+    expr t5 = f(a, a);
+    lean_assert(t3 != t4);
+    lean_assert(t4 != t5);
+    lean_assert(!u.is_modulo_eq(t3, t4));
+    lean_assert(!u.is_modulo_eq(t4, t5));
+    u.assign(m2, a);
+    lean_assert(u.is_modulo_eq(t3, t4));
+    lean_assert(u.is_modulo_eq(t4, t5));
+    lean_assert(u.is_modulo_eq(g(t3, m1), g(t4, a)));
+    lean_assert(!u.is_modulo_eq(g(t3, m3), g(t4, b)));
+    u.assign(m3, b);
+    lean_assert(u.is_modulo_eq(g(t3, m3), g(t4, b)));
+    std::cout << u << "\n";
+    expr m4 = u.mk_metavar();
+    std::cout << u << "\n";
+    u.assign(m4, m1);
+    std::cout << u << "\n";
+    expr m5 = u.mk_metavar();
+    expr m6 = u.mk_metavar();
+    u.assign(m5, m6);
+    metavar_env u2(u);
+    u.assign(m5, m3);
+    std::cout << u << "\n";
+    u2.assign(m5, m2);
+    std::cout << u2 << "\n";
+}
+
+static void tst3() {
+    environment env;
+    metavar_env uenv(env);
+    expr m1 = uenv.mk_metavar();
+    expr f  = Const("f");
+    expr a  = Const("a");
+    expr b  = Const("b");
+    expr g  = Const("g");
+    expr m2 = uenv.mk_metavar();
+    uenv.assign(m2, f(m1, a));
+    uenv.assign(m1, b);
+    std::cout << uenv.instantiate_metavars(g(m2,b)) << "\n";
+    lean_assert(uenv.instantiate_metavars(g(m2,b)) == g(f(b,a), b));
+    lean_assert(uenv.instantiate_metavars(g(m2,f(a,m1))) == g(f(b,a),f(a,b)));
+    expr m3 = uenv.mk_metavar();
+    expr m4 = uenv.mk_metavar();
+    uenv.assign(m3, f(m4));
+    try {
+        uenv.assign(m4, f(m3));
+        lean_unreachable();
+    } catch (exception) {
+    }
+}
+
+static void tst4() {
+    environment env;
+    metavar_env uenv(env);
+    expr m1 = uenv.mk_metavar();
+    expr m2 = uenv.mk_metavar();
+    uenv.assign(m1, m2);
+    expr f  = Const("f");
+    expr a  = Const("a");
+    expr t  = uenv.instantiate_metavars(f(m1,f(a, m1)));
+    std::cout << t << "\n";
+    lean_assert(t == f(m2, f(a, m2)));
+}
+
+static void tst5() {
+    environment env;
+    env.add_var("A", Type());
+    env.add_var("B", Type());
+    expr A  = Const("A");
+    expr B  = Const("B");
+    env.add_definition("F", Type(), A >> B);
+    env.add_definition("G", Type(), B >> B);
+    metavar_env uenv(env);
+    expr m1 = uenv.mk_metavar();
+    expr m2 = uenv.mk_metavar();
+    expr m3 = uenv.mk_metavar();
+    expr m4 = uenv.mk_metavar();
+    expr F  = Const("F");
+    expr G  = Const("G");
+    expr f  = Const("f");
+    expr g  = Const("g");
+    expr a  = Const("a");
+    expr b  = Const("b");
+    expr x  = Const("x");
+    expr Id = Fun({x, A}, x);
+    expr t1 = f(m1, g(a, F));
+    expr t2 = f(g(a, b), Id(g(m2, m3 >> m4)));
+    metavar_env uenv2(uenv);
+    uenv2.unify(t1, t2);
+    std::cout << uenv2 << "\n";
+    lean_assert(uenv2.root(m1) == g(a, b));
+    lean_assert(uenv2.root(m2) == a);
+    lean_assert(uenv2.root(m3) == A);
+    lean_assert(uenv2.root(m4) == B);
+    lean_assert(uenv2.instantiate_metavars(t1) == f(g(a, b), g(a, F)));
+    lean_assert(uenv2.instantiate_metavars(t2) == f(g(a, b), Id(g(a, A >> B))));
+    metavar_env uenv3(uenv);
+    expr t3 = f(m1, m1 >> m1);
+    expr t4 = f(m2 >> m2, m3);
+    uenv3.unify(t3, t4);
+    std::cout << uenv3 << "\n";
+    uenv3.unify(m1, G);
+    std::cout << uenv3 << "\n";
+    std::cout << uenv3.instantiate_metavars(t3) << "\n";
+}
+
+static void tst6() {
+    environment env;
+    env.add_var("A", Type());
+    expr A = Const("A");
+    expr f = Const("f");
+    expr g = Const("g");
+    expr a = Const("a");
+    expr b = Const("b");
+    context ctx1;
+    ctx1 = extend(extend(ctx1, "x", A >> A), "y", A);
+    metavar_env uenv(env);
+    expr m1 = uenv.mk_metavar();
+    expr m2 = uenv.mk_metavar(ctx1);
+    context ctx2;
+    ctx2 = extend(ctx2, "x", m1);
+    expr m3 = uenv.mk_metavar(ctx2);
+    metavar_env uenv2(uenv);
+    expr t1 = f(m2,    m3);
+    expr t2 = f(g(m3), Var(0));
+    std::cout << "----------------\n";
+    std::cout << uenv << "\n";
+    uenv.unify(t1, t2);
+    std::cout << uenv << "\n";
+    std::cout << uenv.instantiate_metavars(t1) << "\n";
+    std::cout << uenv.instantiate_metavars(t2) << "\n";
+    lean_assert(uenv.instantiate_metavars(t1) == uenv.instantiate_metavars(t2));
+    lean_assert(uenv.instantiate_metavars(t2) == f(g(Var(0)), Var(0)));
+    lean_assert(uenv.instantiate_metavars(m1) == A >> A);
+    expr t3 = f(m2);
+    expr t4 = f(m3);
+    uenv2.unify(t3, t4);
+    std::cout << "----------------\n";
+    std::cout << uenv2 << "\n";
+    lean_assert(uenv2.instantiate_metavars(m1) == A >> A);
+    lean_assert(length(uenv2.get_context(m2)) == length(uenv2.get_context(m3)));
+}
+
+static void tst7() {
+    environment env;
+    env.add_var("A", Type());
+    env.add_var("B", Type());
+    expr A  = Const("A");
+    expr B  = Const("B");
+    env.add_definition("F", Type(), A >> B);
+    env.add_definition("G", Type(), B >> B);
+    name_set S;
+    S.insert("G");
+    metavar_env uenv(env, &S);
+    expr m1 = uenv.mk_metavar();
+    expr m2 = uenv.mk_metavar();
+    expr m3 = uenv.mk_metavar();
+    expr m4 = uenv.mk_metavar();
+    expr F  = Const("F");
+    expr G  = Const("G");
+    expr f  = Const("f");
+    expr g  = Const("g");
+    expr a  = Const("a");
+    expr b  = Const("b");
+    expr x  = Const("x");
+    expr Id = Fun({x, A}, x);
+    expr t1 = f(m1, g(a, F));
+    expr t2 = f(g(a, b), Id(g(m2, m3 >> m4)));
+    metavar_env uenv2(uenv);
+    try {
+        uenv2.unify(t1, t2);
+        lean_unreachable();
+    } catch (exception) {
+        // It failed because "F" is not in the set of
+        // available definitions.
+    }
+    S.insert("F");
+    uenv.unify(t1, t2);
+    std::cout << uenv.instantiate_metavars(t1) << "\n";
+    std::cout << uenv.instantiate_metavars(t2) << "\n";
+}
+
+static void tst8() {
+    environment env;
+    elaborator  elb(env);
+    expr A = Const("A");
+    expr B = Const("B");
+    expr F = Const("F");
+    expr g = Const("g");
+    expr a = Const("a");
+    expr Nat  = Const("Nat");
+    expr Real = Const("Real");
+    env.add_var("Nat", Type());
+    env.add_var("Real", Type());
+    env.add_var("F", Pi({{A, Type()}, {B, Type()}, {g, A >> B}}, A));
+    env.add_var("f", Nat >> Real);
+    std::cout << "--------------------\n" << env << "\n";
+    expr _ = mk_placholder();
+    expr f = Const("f");
+    expr t = F(_,_,f);
+    std::cout << elaborate(elb, t) << "\n";
+    lean_assert(elaborate(elb, t) == F(Nat, Real, f));
+}
+
+static void tst9() {
+    environment env = mk_toplevel();
+    elaborator  elb(env);
+    expr a  = Const("a");
+    expr b  = Const("b");
+    expr c  = Const("c");
+    expr H1 = Const("H1");
+    expr H2 = Const("H2");
+    env.add_var("a", Bool);
+    env.add_var("b", Bool);
+    env.add_var("c", Bool);
+    env.add_axiom("H1", Eq(a, b));
+    env.add_axiom("H2", Eq(b, c));
+    expr _ = mk_placholder();
+    expr t = Trans(_,_,_,_,H1,H2);
+    expr new_t = elb(elaborate(elb, t));
+    std::cout << new_t << "\n";
+    lean_assert(new_t == Trans(Bool,a,b,c,H1,H2));
+}
+
+static void tst10() {
+    environment env = mk_toplevel();
+    elaborator  elb(env);
+    expr Nat = Const("Nat");
+    env.add_var("Nat", Type());
+    env.add_var("vec", Nat >> Type());
+    expr n   = Const("n");
+    expr vec = Const("vec");
+    env.add_var("f", Pi({n, Nat}, vec(n) >> Nat));
+    expr f = Const("f");
+    expr a = Const("a");
+    expr b = Const("b");
+    expr H = Const("H");
+    expr fact = Const("fact");
+    env.add_var("a", Nat);
+    env.add_var("b", Nat);
+    env.add_definition("fact", Bool, Eq(a, b));
+    env.add_axiom("H", fact);
+    expr _ = mk_placholder();
+    expr t = Congr2(_,_,_,_,f,H);
+    std::cout << elaborate(elb, t) << "\n";
+    lean_assert(elaborate(elb,t) == Congr2(Nat, Fun({n,Nat}, vec(n) >> Nat), a, b, f, H));
+}
+
+static void tst11() {
+    environment env;
+    elaborator  elb(env);
+    expr Nat = Const("Nat");
+    env.add_var("Nat", Type());
+    expr R   = Const("R");
+    env.add_var("R", Type());
+    env.add_var("a", Nat);
+    expr a   = Const("a");
+    expr f   = Const("f");
+    env.add_var("f", Nat >> ((R >> Nat) >> R));
+    expr x   = Const("x");
+    expr y   = Const("y");
+    expr _ = mk_placholder();
+    expr t = Fun({{x,_},{y,_}}, f(x, y));
+    std::cout << t << "\n";
+    std::cout << elaborate(elb, t) << "\n";
+}
+
+static void tst12() {
+    environment env;
+    elaborator  elb(env);
+    expr A = Const("A");
+    expr B = Const("B");
+    expr a = Const("a");
+    expr b = Const("b");
+    expr f = Const("f");
+    expr g = Const("g");
+    expr Nat = Const("Nat");
+    env.add_var("Nat", Type());
+    env.add_var("f", Pi({{A,Type()},{a,A},{b,A}}, A));
+    env.add_var("g", Nat >> Nat);
+    expr _ = mk_placholder();
+    expr t = Fun({{a,_},{b,_}},g(f(_,a,b)));
+    std::cout << elaborate(elb, t) << "\n";
+    lean_assert(elaborate(elb, t) == Fun({{a,Nat},{b,Nat}},g(f(Nat,a,b))));
+}
+
+static void tst13() {
+    environment env;
+    elaborator  elb(env);
+    expr lst  = Const("list");
+    expr nil  = Const("nil");
+    expr cons = Const("cons");
+    expr N    = Const("N");
+    expr A    = Const("A");
+    expr f    = Const("f");
+    expr l    = Const("l");
+    expr a    = Const("a");
+    env.add_var("N", Type());
+    env.add_var("list", Type() >> Type());
+    env.add_var("nil", Pi({A, Type()}, lst(A)));
+    env.add_var("cons", Pi({{A, Type()}, {a, A}, {l, lst(A)}}, lst(A)));
+    env.add_var("f", lst(N>>N) >> Bool);
+    expr _ = mk_placholder();
+    expr t = Fun({a,_}, f(cons(_, a, cons(_, a, nil(_)))));
+    std::cout << elaborate(elb, t) << "\n";
+}
+
+static void tst14() {
+    environment env;
+    elaborator  elb(env);
+    expr x = Const("x");
+    expr _ = mk_placholder();
+    expr omega = mk_app(Fun({x,_}, x(x)), Fun({x,_}, x(x)));
+    try {
+        elaborate(elb, omega);
+        lean_unreachable();
+    } catch (exception ex) {
+    }
+}
+
+int main() {
+    tst1();
+    tst2();
+    tst3();
+    tst4();
+    tst5();
+    tst6();
+    tst7();
+    tst8();
+    tst9();
+    tst10();
+    tst11();
+    tst12();
+    tst13();
+    tst14();
+    return has_violations() ? 1 : 0;
+}