diff --git a/src/frontends/lean/pp.cpp b/src/frontends/lean/pp.cpp
index 99d16c9b8..e0ee6b92d 100644
--- a/src/frontends/lean/pp.cpp
+++ b/src/frontends/lean/pp.cpp
@@ -16,6 +16,7 @@ Author: Leonardo de Moura
 #include "util/interrupt.h"
 #include "kernel/context.h"
 #include "kernel/for_each_fn.h"
+#include "kernel/find_fn.h"
 #include "kernel/occurs.h"
 #include "kernel/builtin.h"
 #include "kernel/free_vars.h"
@@ -1119,26 +1120,13 @@ class pp_fn {
         m_alias_min_weight = get_pp_alias_min_weight(opts);
     }
 
-
-    struct found_prefix {};
     bool uses_prefix(expr const & e, name const & prefix) {
-        auto f = [&](expr const & e, unsigned) {
-            if (is_constant(e)) {
-                if (is_prefix_of(prefix, const_name(e))) throw found_prefix();
-            } else if (is_abstraction(e)) {
-                if (is_prefix_of(prefix, abst_name(e))) throw found_prefix();
-            } else if (is_let(e)) {
-                if (is_prefix_of(prefix, let_name(e))) throw found_prefix();
-            }
-            return true;
-        };
-        try {
-            for_each_fn<decltype(f)> visitor(f);
-            visitor(e);
-            return false;
-        } catch (found_prefix) {
-            return true;
-        }
+        return find(e, [&](expr const & e) {
+                return
+                    (is_constant(e) && is_prefix_of(prefix, const_name(e)))   ||
+                    (is_abstraction(e) && is_prefix_of(prefix, abst_name(e))) ||
+                    (is_let(e) && is_prefix_of(prefix, let_name(e)));
+            });
     }
 
     name find_unused_prefix(expr const & e) {
diff --git a/src/kernel/CMakeLists.txt b/src/kernel/CMakeLists.txt
index 3aa0ae7d4..f5a0853b3 100644
--- a/src/kernel/CMakeLists.txt
+++ b/src/kernel/CMakeLists.txt
@@ -1,7 +1,7 @@
 add_library(kernel expr.cpp free_vars.cpp abstract.cpp instantiate.cpp
   normalizer.cpp context.cpp level.cpp object.cpp environment.cpp
   type_checker.cpp builtin.cpp occurs.cpp metavar.cpp justification.cpp
-  unification_constraint.cpp printer.cpp formatter.cpp has_cached_type.cpp
+  unification_constraint.cpp printer.cpp formatter.cpp
   kernel_exception.cpp type_checker_justification.cpp pos_info_provider.cpp
   replace_visitor.cpp)
 
diff --git a/src/kernel/environment.cpp b/src/kernel/environment.cpp
index d5d0cd64c..58c4b3d8b 100644
--- a/src/kernel/environment.cpp
+++ b/src/kernel/environment.cpp
@@ -15,12 +15,12 @@ Author: Leonardo de Moura
 #include "util/safe_arith.h"
 #include "util/realpath.h"
 #include "kernel/for_each_fn.h"
+#include "kernel/find_fn.h"
 #include "kernel/kernel_exception.h"
 #include "kernel/environment.h"
 #include "kernel/threadsafe_environment.h"
 #include "kernel/type_checker.h"
 #include "kernel/normalizer.h"
-#include "kernel/has_cached_type.h"
 
 namespace lean {
 static name g_builtin_module("builtin_module");
@@ -288,8 +288,16 @@ struct environment::imp {
         m_uvars.emplace_back();
     }
 
+    /**
+       The kernel should *not* accept expressions containing cached types.
+       Reason: Cached types may introduce unsoundness.
+       For example, in the environment env, the constant x may have type T.
+       Now suppose we are trying to add a new definition D that contains x,
+       and x is associated with a cached type T'. The cached type may allow
+       us to accept a definition that is type incorrect with respect to env.
+    */
     void check_no_cached_type(expr const & e, environment const & env) {
-        if (has_cached_type(e))
+        if (find(e, [](expr const & a) { return is_constant(a) && const_type(a); }))
             throw kernel_exception(env, "expression has a constant with a cached type, this is a bug in one of Lean tactics and/or solvers");
     }
 
diff --git a/src/kernel/find_fn.h b/src/kernel/find_fn.h
new file mode 100644
index 000000000..37302a115
--- /dev/null
+++ b/src/kernel/find_fn.h
@@ -0,0 +1,67 @@
+/*
+Copyright (c) 2013 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/for_each_fn.h"
+#include "kernel/context.h"
+
+namespace lean {
+template<typename P>
+class find_fn {
+    struct pred_fn {
+        expr & m_result;
+        P      m_p;
+        pred_fn(expr & result, P const & p):m_result(result), m_p(p) {}
+        bool operator()(expr const & e, unsigned) {
+            if (m_result) {
+                return false; // already found result, stop the search
+            } else if (m_p(e)) {
+                m_result = e;
+                return false; // stop the search
+            } else {
+                return true; // continue the search
+            }
+        }
+    };
+    expr                 m_result;
+    for_each_fn<pred_fn> m_proc;
+public:
+    find_fn(P const & p):m_proc(pred_fn(m_result, p)) {}
+    expr operator()(expr const & e) { m_proc(e); return m_result; }
+};
+
+/**
+   \brief Return a subexpression of \c e that satisfies the predicate \c p.
+   If there is none, then return the null expression.
+*/
+template<typename P>
+expr find(expr const & e, P p) {
+    return find_fn<P>(p)(e);
+}
+
+/**
+   \brief Return an expression \c e that satisfies \c p and occurs in \c c or \c es.
+*/
+template<typename P>
+expr find(context const * c, unsigned sz, expr const * es, P p) {
+    find_fn<P> finder(p);
+    if (c) {
+        for (auto const & e : *c) {
+            if (expr r = finder(e.get_domain())) {
+                return r;
+            } else if (e.get_body()) {
+                if (expr r = finder(e.get_body()))
+                    return r;
+            }
+        }
+    }
+    for (unsigned i = 0; i < sz; i++) {
+        if (expr r = finder(es[i]))
+            return r;
+    }
+    return expr();
+}
+}
diff --git a/src/kernel/for_each_fn.h b/src/kernel/for_each_fn.h
index f93c3a9eb..8a6b02efd 100644
--- a/src/kernel/for_each_fn.h
+++ b/src/kernel/for_each_fn.h
@@ -107,4 +107,9 @@ public:
     for_each_fn(F const & f):m_f(f) {}
     void operator()(expr const & e) { apply(e, 0); }
 };
+
+template<typename F>
+void for_each(expr const & e, F f) {
+    return for_each_fn<F>(f)(e);
+}
 }
diff --git a/src/kernel/has_cached_type.cpp b/src/kernel/has_cached_type.cpp
deleted file mode 100644
index 9cec1f7e8..000000000
--- a/src/kernel/has_cached_type.cpp
+++ /dev/null
@@ -1,27 +0,0 @@
-/*
-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 "kernel/expr.h"
-#include "kernel/for_each_fn.h"
-
-namespace lean {
-bool has_cached_type(expr const & e) {
-    bool result = false;
-    auto f = [&](expr const & e, unsigned) {
-        if (result) {
-            return false; // do not continue the search
-        } else if (is_constant(e) && const_type(e)) {
-            result = true;
-            return false;
-        } else {
-            return true;
-        }
-    };
-    for_each_fn<decltype(f)> proc(f);
-    proc(e);
-    return result;
-}
-}
diff --git a/src/kernel/has_cached_type.h b/src/kernel/has_cached_type.h
deleted file mode 100644
index eba6a15cc..000000000
--- a/src/kernel/has_cached_type.h
+++ /dev/null
@@ -1,22 +0,0 @@
-/*
-Copyright (c) 2013 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/expr.h"
-
-namespace lean {
-/**
-   \brief Return true iff \c e contains a constant with a cached type.
-
-   The kernel should *not* accept expressions containing cached types.
-   Reason: Cached types may introduce unsoundness.
-   For example, in the environment env, the constant x may have type T.
-   Now suppose we are trying to add a new definition D that contains x,
-   and x is associated with a cached type T'. The cached type may allow
-   us to accept a definition that is type incorrect with respect to env.
-*/
-bool has_cached_type(expr const & e);
-}
diff --git a/src/kernel/metavar.cpp b/src/kernel/metavar.cpp
index dd555814f..4c1380122 100644
--- a/src/kernel/metavar.cpp
+++ b/src/kernel/metavar.cpp
@@ -14,6 +14,7 @@ Author: Leonardo de Moura
 #include "kernel/instantiate.h"
 #include "kernel/occurs.h"
 #include "kernel/for_each_fn.h"
+#include "kernel/find_fn.h"
 
 namespace lean {
 /**
@@ -289,19 +290,17 @@ bool has_assigned_metavar(expr const & e, metavar_env const & menv) {
         return false;
     } else {
         bool result = false;
-        auto proc = [&](expr const & n, unsigned) {
-            if (result)
-                return false;
-            if (!has_metavar(n))
-                return false;
-            if (is_metavar(n) && menv.is_assigned(n)) {
-                result = true;
-                return false;
-            }
-            return true;
-        };
-        for_each_fn<decltype(proc)> visitor(proc);
-        visitor(e);
+        for_each(e, [&](expr const & n, unsigned) {
+                if (result)
+                    return false;
+                if (!has_metavar(n))
+                    return false;
+                if (is_metavar(n) && menv.is_assigned(n)) {
+                    result = true;
+                    return false;
+                }
+                return true;
+            });
         return result;
     }
 }
@@ -365,23 +364,12 @@ bool has_metavar(expr const & e, expr const & m, metavar_env const & menv) {
     if (has_metavar(e)) {
         lean_assert(is_metavar(m));
         lean_assert(!menv.is_assigned(m));
-        auto f = [&](expr const & m2, unsigned) {
-            if (is_metavar(m2)) {
-                if (metavar_name(m) == metavar_name(m2))
-                    throw found_metavar();
-                if (menv.is_assigned(m2) &&
-                    has_metavar(menv.get_subst(m2), m, menv))
-                    throw found_metavar();
-            }
-            return true;
-        };
-        try {
-            for_each_fn<decltype(f)> proc(f);
-            proc(e);
-            return false;
-        } catch (found_metavar) {
-            return true;
-        }
+        return find(e, [&](expr const & m2) {
+                return
+                    is_metavar(m2) &&
+                    ((metavar_name(m) == metavar_name(m2)) ||
+                     (menv.is_assigned(m2) && has_metavar(menv.get_subst(m2), m, menv)));
+            });
     } else {
         return false;
     }
diff --git a/src/kernel/occurs.cpp b/src/kernel/occurs.cpp
index ab7b0ad69..4b6e65ede 100644
--- a/src/kernel/occurs.cpp
+++ b/src/kernel/occurs.cpp
@@ -5,57 +5,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #include "kernel/occurs.h"
-#include "kernel/for_each_fn.h"
+#include "kernel/find_fn.h"
 
 namespace lean {
-template<typename F>
-void for_each(F & f, context const * c, unsigned sz, expr const * es) {
-    for_each_fn<F> visitor(f);
-    if (c) {
-        for (auto const & e : *c) {
-            visitor(e.get_domain());
-            if (e.get_body())
-                visitor(e.get_body());
-        }
-    }
-    for (unsigned i = 0; i < sz; i++)
-        visitor(es[i]);
-}
-
-namespace occurs_ns {
-/** \brief Auxiliary struct used to sign (as an exception) that an occurrence was found. */
-struct found {};
-}
 bool occurs(name const & n, context const * c, unsigned sz, expr const * es) {
-    auto visitor = [&](expr const & e, unsigned) -> bool {
-        if (is_constant(e)) {
-            if (const_name(e) == n)
-                throw occurs_ns::found();
-        }
-        return true;
-    };
-    try {
-        for_each(visitor, c, sz, es);
-        return false;
-    } catch (occurs_ns::found) {
-        return true;
-    }
+    return find(c, sz, es, [&](expr const & e) { return is_constant(e) && const_name(e) == n; });
 }
 
 bool occurs(expr const & n, context const * c, unsigned sz, expr const * es) {
-    auto visitor = [&](expr const & e, unsigned) -> bool {
-        if (e == n)
-            throw occurs_ns::found();
-        return true;
-    };
-    try {
-        for_each(visitor, c, sz, es);
-        return false;
-    } catch (occurs_ns::found) {
-        return true;
-    }
+    return find(c, sz, es, [&](expr const & e) { return e == n; });
 }
-
 bool occurs(expr const & n, expr const & m) { return occurs(n, nullptr, 1, &m); }
 bool occurs(name const & n, expr const & m) { return occurs(n, nullptr, 1, &m); }
 bool occurs(expr const & n, context const & c) { return occurs(n, &c, 0, nullptr); }