diff --git a/src/kernel/replace.h b/src/kernel/replace.h
index 1925c570a..1641f91a1 100644
--- a/src/kernel/replace.h
+++ b/src/kernel/replace.h
@@ -9,6 +9,15 @@ Author: Leonardo de Moura
 #include "expr.h"
 #include "expr_maps.h"
 namespace lean {
+/**
+   \brief Default replace_fn postprocessor functional object. It is a
+   do-nothing object.
+*/
+class default_replace_postprocessor {
+public:
+    void operator()(expr const & old_e, expr const & new_e) {}
+};
+
 /**
    \brief Functional for applying <tt>F</tt> to the subexpressions of a given expression.
 
@@ -18,13 +27,17 @@ namespace lean {
    F is invoked for each subexpression \c s of the input expression e.
    In a call <tt>F(n, s)</tt>, n is the scope level, i.e., the number of
    bindings operators that enclosing \c s.
+
+   P is a "post-processing" functional object that is applied to each
+   pair (old, new)
 */
-template<typename F>
+template<typename F, typename P=default_replace_postprocessor>
 class replace_fn {
     static_assert(std::is_same<typename std::result_of<F(expr const &, unsigned)>::type, expr>::value,
                   "replace_fn: return type of F is not expr");
     expr_cell_offset_map<expr> m_cache;
     F                          m_f;
+    P                          m_post;
 
     expr apply(expr const & e, unsigned offset) {
         bool sh = false;
@@ -60,12 +73,15 @@ class replace_fn {
         if (sh)
             m_cache.insert(std::make_pair(expr_cell_offset(e.raw(), offset), r));
 
+        m_post(e, r);
+
         return r;
     }
 
 public:
-    replace_fn(F const & f):
-        m_f(f) {
+    replace_fn(F const & f, P const & p = P()):
+        m_f(f),
+        m_post(p) {
     }
 
     expr operator()(expr const & e) {
diff --git a/src/tests/kernel/replace.cpp b/src/tests/kernel/replace.cpp
index 8dd1ad0f9..6389c6d39 100644
--- a/src/tests/kernel/replace.cpp
+++ b/src/tests/kernel/replace.cpp
@@ -8,6 +8,8 @@ Author: Leonardo de Moura
 #include "abstract.h"
 #include "instantiate.h"
 #include "deep_copy.h"
+#include "expr_maps.h"
+#include "replace.h"
 #include "printer.h"
 #include "name.h"
 #include "test.h"
@@ -44,9 +46,63 @@ static void tst2() {
     lean_assert(instantiate(mk_pi("_", Var(3), Var(4)), Var(0)) == mk_pi("_", Var(2), Var(3)));
 }
 
+class tracer {
+    expr_map<expr> & m_trace;
+public:
+    tracer(expr_map<expr> & trace):m_trace(trace) {}
+
+    void operator()(expr const & old_e, expr const & new_e) {
+        if (!is_eqp(new_e, old_e)) {
+            m_trace[new_e] = old_e;
+        }
+    }
+};
+
+static void tst3() {
+    expr f = Const("f");
+    expr x = Const("x");
+    expr y = Const("y");
+    expr c = Const("c");
+    expr d = Const("d");
+    expr A = Const("A");
+    expr_map<expr> trace;
+    auto proc = [&](expr const & x, unsigned offset) -> expr {
+        if (is_var(x)) {
+            unsigned vidx = var_idx(x);
+            if (vidx == offset)
+                return c;
+            else if (vidx > offset)
+                return mk_var(vidx-1);
+            else
+                return x;
+        } else {
+            return x;
+        }
+    };
+    replace_fn<decltype(proc), tracer> replacer(proc, tracer(trace));
+    expr t = Fun({{x, A}, {y, A}}, f(x, f(f(f(x,x), f(y, d)), f(d, d))));
+    expr b = abst_body(t);
+    expr r = replacer(b);
+    std::cout << r << "\n";
+    lean_assert(r == Fun({y, A}, f(c, f(f(f(c,c), f(y, d)), f(d, d)))));
+    for (auto p : trace) {
+        std::cout << p.first << " --> " << p.second << "\n";
+    }
+    lean_assert(trace[c] == Var(1));
+    std::cout << arg(arg(abst_body(r), 2), 2) << "\n";
+    lean_assert(arg(arg(abst_body(r), 2), 2) == f(d,d));
+    lean_assert(trace.find(arg(arg(abst_body(r), 2), 2)) == trace.end());
+    lean_assert(trace.find(abst_body(r)) != trace.end());
+    lean_assert(trace.find(arg(abst_body(r), 2)) != trace.end());
+    lean_assert(trace.find(arg(arg(abst_body(r), 2), 1)) != trace.end());
+    lean_assert(trace.find(arg(arg(arg(abst_body(r), 2), 1), 1)) != trace.end());
+    lean_assert(trace.find(arg(arg(arg(abst_body(r), 2), 1), 2)) == trace.end());
+}
+
 int main() {
     tst1();
     tst2();
+    tst3();
     std::cout << "done" << "\n";
     return has_violations() ? 1 : 0;
 }