diff --git a/src/library/compiler/CMakeLists.txt b/src/library/compiler/CMakeLists.txt
index 6049541f68..e9c6195680 100644
--- a/src/library/compiler/CMakeLists.txt
+++ b/src/library/compiler/CMakeLists.txt
@@ -2,5 +2,5 @@ add_library(compiler OBJECT
   emit_bytecode.cpp init_module.cpp
   ## New compiler
   util.cpp lcnf.cpp csimp.cpp elim_dead_let.cpp cse.cpp erase_irrelevant.cpp
-  specialize.cpp compiler.cpp lambda_lifting.cpp extract_closed.cpp llnf.cpp
-  ir.cpp)
+  specialize.cpp compiler.cpp lambda_lifting.cpp extract_closed.cpp
+  simp_app_args.cpp llnf.cpp ir.cpp)
diff --git a/src/library/compiler/compiler.cpp b/src/library/compiler/compiler.cpp
index 9841bc13cd..f5dc535ea4 100644
--- a/src/library/compiler/compiler.cpp
+++ b/src/library/compiler/compiler.cpp
@@ -19,6 +19,7 @@ Author: Leonardo de Moura
 #include "library/compiler/specialize.h"
 #include "library/compiler/lambda_lifting.h"
 #include "library/compiler/extract_closed.h"
+#include "library/compiler/simp_app_args.h"
 #include "library/compiler/llnf.h"
 #include "library/compiler/emit_bytecode.h"
 
@@ -87,10 +88,11 @@ static environment cache_stage1(environment env, comp_decls const & ds) {
 static environment cache_stage2(environment env, comp_decls const & ds) {
     for (comp_decl const & d : ds) {
         name n = d.fst();
+        expr t = mk_enf_object_type(); // TODO(Leo): make it more precise
         expr v = d.snd();
         /* This a temporary hack to store Stage2 intermediate result.
            We should not store this information as a declaration. */
-        declaration aux_decl = mk_definition(mk_cstage2_name(n), names(), mk_enf_object_type(),
+        declaration aux_decl = mk_definition(mk_cstage2_name(n), names(), t,
                                              v, reducibility_hints::mk_opaque(), true);
         env = module::add(env, aux_decl, false);
     }
@@ -151,6 +153,10 @@ environment compile(environment const & env, options const & opts, names const &
     trace_compiler(name({"compiler", "stage2"}), ds);
     ds = apply(esimp, new_env, ds);
     trace_compiler(name({"compiler", "simp"}), ds);
+    ds = apply(simp_app_args, new_env, ds);
+    ds = apply(ecse, new_env, ds);
+    ds = apply(elim_dead_let, ds);
+    trace_compiler(name({"compiler", "simp_app_args"}), ds);
     lean_trace(name({"compiler", "boxed"}),
                auto to_llnf_unbox  = [&](environment const & env, expr const & e) { return to_llnf(env, e, true); };
                auto aux_ds = apply(to_llnf_unbox, new_env, ds);
@@ -182,6 +188,7 @@ void initialize_compiler() {
     register_trace_class({"compiler", "erase_irrelevant"});
     register_trace_class({"compiler", "lambda_lifting"});
     register_trace_class({"compiler", "extract_closed"});
+    register_trace_class({"compiler", "simp_app_args"});
     register_trace_class({"compiler", "llnf"});
     register_trace_class({"compiler", "boxed"});
     register_trace_class({"compiler", "optimize_bytecode"});
diff --git a/src/library/compiler/simp_app_args.cpp b/src/library/compiler/simp_app_args.cpp
new file mode 100644
index 0000000000..25508a478b
--- /dev/null
+++ b/src/library/compiler/simp_app_args.cpp
@@ -0,0 +1,137 @@
+/*
+Copyright (c) 2018 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "kernel/instantiate.h"
+#include "library/compiler/util.h"
+
+namespace lean {
+/* Make sure every argument of applications and projections is a free variable (or neutral element). */
+class simp_app_args_fn {
+    type_checker::state m_st;
+    local_ctx           m_lctx;
+    buffer<expr>        m_fvars;
+    name                m_x;
+    unsigned            m_next_idx{1};
+
+    environment const & env() const { return m_st.env(); }
+    name_generator & ngen() { return m_st.ngen(); }
+
+    name next_name() {
+        name r = m_x.append_after(m_next_idx);
+        m_next_idx++;
+        return r;
+    }
+
+    expr mk_let(unsigned saved_fvars_size, expr r) {
+        lean_assert(saved_fvars_size <= m_fvars.size());
+        if (saved_fvars_size == m_fvars.size())
+            return r;
+        r = m_lctx.mk_lambda(m_fvars.size() - saved_fvars_size, m_fvars.data() + saved_fvars_size, r);
+        m_fvars.shrink(saved_fvars_size);
+        return r;
+    }
+
+    expr visit_let(expr e) {
+        buffer<expr> curr_fvars;
+        while (is_let(e)) {
+            lean_assert(!has_loose_bvars(let_type(e)));
+            expr t     = let_type(e);
+            expr v     = visit(instantiate_rev(let_value(e), curr_fvars.size(), curr_fvars.data()));
+            name n     = let_name(e);
+            if (is_internal_name(n) && !is_join_point_name(n)) {
+                n = next_name();
+            }
+            expr fvar  = m_lctx.mk_local_decl(ngen(), n, t, v);
+            curr_fvars.push_back(fvar);
+            m_fvars.push_back(fvar);
+            e = let_body(e);
+        }
+        return visit(instantiate_rev(e, curr_fvars.size(), curr_fvars.data()));
+    }
+
+    expr visit_lambda(expr e) {
+        buffer<expr> binding_fvars;
+        while (is_lambda(e)) {
+            lean_assert(!has_loose_bvars(binding_domain(e)));
+            expr new_fvar = m_lctx.mk_local_decl(ngen(), binding_name(e), binding_domain(e), binding_info(e));
+            binding_fvars.push_back(new_fvar);
+            e = binding_body(e);
+        }
+        e = instantiate_rev(e, binding_fvars.size(), binding_fvars.data());
+        unsigned saved_fvars_size = m_fvars.size();
+        expr r = mk_let(saved_fvars_size, visit(e));
+        lean_assert(!is_lambda(r));
+        return m_lctx.mk_lambda(binding_fvars, r);
+    }
+
+    expr ensure_simple_arg(expr const & e) {
+        if (is_fvar(e) || is_enf_neutral(e)) {
+            return e;
+        } else if (is_lit(e)) {
+            expr fvar  = m_lctx.mk_local_decl(ngen(), next_name(), mk_enf_object_type(), e);
+            m_fvars.push_back(fvar);
+            return fvar;
+        } else if (is_constant(e)) {
+            expr type;
+            if (optional<constant_info> info = env().find(const_name(e)))
+                type = mk_runtime_type(m_st, m_lctx, info->get_type());
+            else
+                type = mk_enf_object_type(); // TODO(Leo): improve
+            expr fvar = m_lctx.mk_local_decl(ngen(), next_name(), type, e);
+            m_fvars.push_back(fvar);
+            return fvar;
+        } else {
+            lean_unreachable();
+        }
+    }
+
+    expr visit_proj(expr const & e) {
+        expr arg = ensure_simple_arg(proj_expr(e));
+        return update_proj(e, arg);
+    }
+
+    expr visit_app(expr const & e) {
+        buffer<expr> args;
+        expr const & fn = get_app_args(e, args);
+        if (is_cases_on_app(env(), e)) {
+            args[0] = ensure_simple_arg(args[0]);
+            for (unsigned i = 1; i < args.size(); i++) {
+                if (is_lambda(args[i])) {
+                    args[i] = visit(args[i]);
+                } else {
+                    unsigned saved_fvars_size = m_fvars.size();
+                    args[i] = mk_let(saved_fvars_size, visit(args[i]));
+                }
+            }
+        } else {
+            for (expr & arg : args)
+                arg = ensure_simple_arg(arg);
+        }
+        return mk_app(fn, args);
+    }
+
+    expr visit(expr const & e) {
+        switch (e.kind()) {
+        case expr_kind::App:    return visit_app(e);
+        case expr_kind::Lambda: return visit_lambda(e);
+        case expr_kind::Let:    return visit_let(e);
+        case expr_kind::Proj:   return visit_proj(e);
+        default:                return e;
+        }
+    }
+
+public:
+    simp_app_args_fn(environment const & env):m_st(env), m_x("_x") {}
+
+    expr operator()(expr const & e) {
+        return mk_let(0, visit(e));
+    }
+};
+
+expr simp_app_args(environment const & env, expr const & e) {
+    return simp_app_args_fn(env)(e);
+}
+}
diff --git a/src/library/compiler/simp_app_args.h b/src/library/compiler/simp_app_args.h
new file mode 100644
index 0000000000..af9bb6e1d7
--- /dev/null
+++ b/src/library/compiler/simp_app_args.h
@@ -0,0 +1,11 @@
+/*
+Copyright (c) 2018 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#pragma once
+#include "kernel/environment.h"
+namespace lean {
+expr simp_app_args(environment const & env, expr const & e);
+}