diff --git a/src/library/compiler/erase_irrelevant.cpp b/src/library/compiler/erase_irrelevant.cpp
index 0b57111cec..62bda6e510 100644
--- a/src/library/compiler/erase_irrelevant.cpp
+++ b/src/library/compiler/erase_irrelevant.cpp
@@ -282,9 +282,28 @@ class erase_irrelevant_fn : public compiler_step_visitor {
         return add_args(r, 3, args);
     }
 
+    expr visit_monad_bind(expr const & e, buffer<expr> const & args) {
+        if (args.size() == 6 && is_constant(args[1], get_monadIO_name())) {
+            /* IO bind */
+            expr v = visit(args[4]);
+            expr b = visit(args[5]);
+            /* We just convert it into a let-expression */
+            if (is_lambda(b)) {
+                return mk_let(binding_name(b), mk_neutral_expr(), v, binding_body(b));
+            } else {
+                lean_assert(closed(b));
+                return mk_let(mk_fresh_name(), mk_neutral_expr(), v, mk_app(b, mk_var(0)));
+            }
+        } else {
+            return compiler_step_visitor::visit_app(e);
+        }
+    }
+
     virtual expr visit_app(expr const & e) override {
         if (is_comp_irrelevant(ctx(), e))
             return *g_neutral_expr;
+        if (auto n = to_nat_value(ctx(), e))
+            return *n;
         buffer<expr> args;
         expr const & fn = get_app_args(e, args);
         if (is_lambda(fn)) {
@@ -301,6 +320,8 @@ class erase_irrelevant_fn : public compiler_step_visitor {
                 return visit_quot_mk(args);
             } else if (n == get_subtype_rec_name()) {
                 return visit_subtype_rec(args);
+            } else if (n == get_monad_bind_name()) {
+                return visit_monad_bind(e, args);
             } else if (is_cases_on_recursor(env(), n)) {
                 return visit_cases_on(fn, args);
             } else if (inductive::is_elim_rule(env(), n)) {
diff --git a/src/library/compiler/nat_value.cpp b/src/library/compiler/nat_value.cpp
index d27d9950e5..5e101a32a6 100644
--- a/src/library/compiler/nat_value.cpp
+++ b/src/library/compiler/nat_value.cpp
@@ -81,14 +81,20 @@ mpz const & get_nat_value_value(expr const & e) {
     return static_cast<nat_value_macro const *>(macro_def(e).raw())->get_value();
 }
 
+optional<expr> to_nat_value(type_context & ctx, expr const & e) {
+    if (optional<mpz> v = to_num(e)) {
+        expr type = ctx.whnf(ctx.infer(e));
+        if (is_constant(type, get_nat_name())) {
+            return some_expr(mk_nat_value(*v));
+        }
+    }
+    return none_expr();
+}
+
 class find_nat_values_fn : public compiler_step_visitor {
     expr visit_app(expr const & e) override {
-        if (optional<mpz> v = to_num(e)) {
-            expr type = ctx().whnf(ctx().infer(e));
-            if (is_constant(type, get_nat_name())) {
-                return mk_nat_value(*v);
-            }
-        }
+        if (auto v = to_nat_value(ctx(), e))
+            return *v;
         return compiler_step_visitor::visit_app(e);
     }
 public:
diff --git a/src/library/compiler/nat_value.h b/src/library/compiler/nat_value.h
index 7423f3084e..5133fa4a2e 100644
--- a/src/library/compiler/nat_value.h
+++ b/src/library/compiler/nat_value.h
@@ -5,7 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #pragma once
-#include "kernel/environment.h"
+#include "library/type_context.h"
 
 namespace lean {
 /** \brief Replace nat numerals encoded using bit0, bit1, one with an auxiliary nat_value macro.
@@ -18,6 +18,10 @@ bool is_nat_value(expr const & e);
 /** \brief Return the mpz stored in the nat_value macro.
     \pre is_nat_value(e) */
 mpz const & get_nat_value_value(expr const & e);
+
+/** \brief If \c e encodes a nat numeral, then convert it into a nat_value macro */
+optional<expr> to_nat_value(type_context & ctx, expr const & e);
+
 void initialize_nat_value();
 void finalize_nat_value();
 }